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Deck 47: Matrices and Systems of Equations
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Question
Select the order for the following matrix. 
A)2 × 2
B)4 × 4
C)3 × 1
D)4 × 1
E)1 × 4
A)2 × 2
B)4 × 4
C)3 × 1
D)4 × 1
E)1 × 4
Question
Select the augmented matrix for the system of linear equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Select the system of linear equations represented by the following augmented matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. ) 
A)
(-14,-5)
B)
(-14,-5)
C)
(-14,5)
D)
(-5,-14)
E)
(-5,-14)
A)
(-14,-5)
B)
(-14,-5)
C)
(-14,5)D)
(-5,-14)E)
(-5,-14) Question
Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix
A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.
Original Matrix New Row-Equivalent Matrix
A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.
Question
Select the augmented matrix for the system of linear equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Select the system of linear equations represented by the following augmented matrix.(Variables x,y,z,and w are used whenever applicable. ) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Select the order for the following matrix. 
A)4 × 3
B)4 × 2
C)4 × 4
D)3 × 3
E)3 × 4
A)4 × 3
B)4 × 2
C)4 × 4
D)3 × 3
E)3 × 4
Question
Select the order for the following matrix. 
A)2 × 3
B)3 × 1
C)3 × 2
D)3 × 3
E)2 × 2
A)2 × 3
B)3 × 1
C)3 × 2
D)3 × 3
E)2 × 2
Question
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. ) 
A)
(7,0)
B)
(-1,7)
C)
(7,-1)
D)
(7,1)
E)
(7,1)
A)
(7,0)B)
(-1,7)C)
(7,-1)D)
(7,1)E)
(7,1) Question
Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix
A)Add 6 times Row 2 to Row 1.
B)Add 3 times Row 1 to Row 2.
C)Add 6 times Row 1 to Row 2.
D)Add 4 times Row 2 to Row 1.
E)Add 3 times Row 2 to Row 1.
Original Matrix New Row-Equivalent Matrix
A)Add 6 times Row 2 to Row 1.
B)Add 3 times Row 1 to Row 2.
C)Add 6 times Row 1 to Row 2.
D)Add 4 times Row 2 to Row 1.
E)Add 3 times Row 2 to Row 1.
Question
Determine whether the following matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. 
A)Row-echelon form
B)Not in row-echelon form
C)Reduced row-echelon form
A)Row-echelon form
B)Not in row-echelon form
C)Reduced row-echelon form
Question
Select the system of linear equations represented by the following augmented matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z and if applicable. ) 
A)
(56,12,-6)
B)
(44,0,-6)
C)
(-40,12,6)
D)
(44,0,-6)
E)
(-40,12,6)
A)
(56,12,-6)B)
(44,0,-6)C)
(-40,12,6)D)
(44,0,-6)E)
(-40,12,6) Question
Select the augmented matrix for the system of linear equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the sequence of row operations on the following matrix. Add -3 times R1 to R2. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the sequence of row operations on the following matrix. Add R3 to R4. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. 
A)(-6,7)
B)(-6,5)
C)(-5,6)
D)(5,-6)
E)(6,5)
A)(-6,7)
B)(-6,5)
C)(-5,6)
D)(5,-6)
E)(6,5)
Question
Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. 
A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
Question
Determine the order of the matrix. 
A)1 × 1
B)3
C)3 × 3
D)3 × 1
E)1 × 3
A)1 × 1
B)3
C)3 × 3
D)3 × 1
E)1 × 3
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(-5,-5,4)
B)(5,-5,-4)
C)(-5,-5,-4)
D)(5,5,4)
E)(5,-5,4)
A)(-5,-5,4)
B)(5,-5,-4)
C)(-5,-5,-4)
D)(5,5,4)
E)(5,-5,4)
Question
Write the augmented matrix for the system of linear equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The currents in an electrical network are given by the solution of the system 
where I1,I2 and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 5,I2 = 4,I3 = 8
B)I1 = 4,I2 = 4,I3 = 8
C)I1 = 3,I2 = 4,I3 = 8
D)I1 = 2,I2 = 4,I3 = 8
E)I1 = 1,I2 = 4,I3 = 8
where I1,I2 and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 5,I2 = 4,I3 = 8
B)I1 = 4,I2 = 4,I3 = 8
C)I1 = 3,I2 = 4,I3 = 8
D)I1 = 2,I2 = 4,I3 = 8
E)I1 = 1,I2 = 4,I3 = 8
Question
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. 
A)(0,8,-6)
B)(8,0,-6)
C)(8,-6,0)
D)(-8,-6,0)
E)(8,6,0)
A)(0,8,-6)
B)(8,0,-6)
C)(8,-6,0)
D)(-8,-6,0)
E)(8,6,0)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)
A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)
Question
Write the matrix in reduced row-echelon form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(10,1)
B)(2,1)
C)(2,-6)
D)(-2,1)
E)(2,-1)
A)(10,1)
B)(2,1)
C)(2,-6)
D)(-2,1)
E)(2,-1)
Question
Fill in the blank using elementary row operations to form a row-equivalent matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. 
A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)
A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)
Question
Use matrices to find the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(3,4)
B)(-3,4)
C)(5,18)
D)(-3,-4)
E)(3,-4)
A)(3,4)
B)(-3,4)
C)(5,18)
D)(-3,-4)
E)(3,-4)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)
A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)
A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)
Question
Determine the order of the matrix. 
A)3 × 3
B)2 × 2
C)3 × 1
D)2 × 3
E)3 × 2
A)3 × 3
B)2 × 2
C)3 × 1
D)2 × 3
E)3 × 2
Question
Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix
New Row-Equivalent Matrix
A)Add 2 times R1 to R2.
B)Add -2 times R1 to R2.
C)Add 2 times R2 to R1.
D)Add -2 times R2 to R1.
E)Add 2 times R1 to R1.
New Row-Equivalent Matrix
A)Add 2 times R1 to R2.
B)Add -2 times R1 to R2.
C)Add 2 times R2 to R1.
D)Add -2 times R2 to R1.
E)Add 2 times R1 to R1.
Question
Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system. 
A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)
A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)(1,4)
B)(3,4)
C)(1,12)
D)(4,1)
E)(12,4)
A)(1,4)
B)(3,4)
C)(1,12)
D)(4,1)
E)(12,4)
Question
Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. ) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. 
A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)x = 5,y = -1,z = -6
B)x = -5,y = -1,z = -6
C)x = -5,y = 1,z = -6
D)x = 1,y = 5,z = 6
E)no solution
A)x = 5,y = -1,z = -6
B)x = -5,y = -1,z = -6
C)x = -5,y = 1,z = -6
D)x = 1,y = 5,z = 6
E)no solution
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)x = 5,y = -2,z = 4
B)x = 2,y = 5,z = -4
C)x = -5,y = -2,z = 4
D)no solution
E)x = -5,y = 2,z = 4
A)x = 5,y = -2,z = 4
B)x = 2,y = 5,z = -4
C)x = -5,y = -2,z = 4
D)no solution
E)x = -5,y = 2,z = 4
Question
Use a system of equations to find the specified equation that passes through the points.Solve the system using matrices. Parabola: y = ax2 + bx + c 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. ) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Perform the sequence of row operations on the matrix.What did the operations accomplish? 
Add -4 times R1 to R2,
Add -1 times R1 to R3,
Add -2 times R2 to R3,
Add -1 times R2 to R1.
A)
The operations produce a row-equivalent matrix in reduced row-echelon form.
B)
The operations produce a row-equivalent matrix in reduced row-echelon form.
C)
The operations produce a row-equivalent matrix in reduced row-echelon form.
D)
The operations produce a row-equivalent matrix in reduced row-echelon form.
E)
The operations produce a row-equivalent matrix in reduced row-echelon form.
Add -4 times R1 to R2,Add -1 times R1 to R3,
Add -2 times R2 to R3,
Add -1 times R2 to R1.
A)
The operations produce a row-equivalent matrix in reduced row-echelon form.B)
The operations produce a row-equivalent matrix in reduced row-echelon form.C)
The operations produce a row-equivalent matrix in reduced row-echelon form.D)
The operations produce a row-equivalent matrix in reduced row-echelon form.E)
The operations produce a row-equivalent matrix in reduced row-echelon form. Question
Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. 
A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3
A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3
Question
Write the augmented matrix for the system of linear equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the matrix in reduced row-echelon form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the order of the matrix. 
A)2 × 3
B)3 × 3
C)3 × 1
D)3 × 2
E)2 × 2
A)2 × 3
B)3 × 3
C)3 × 1
D)3 × 2
E)2 × 2
Question
An augmented matrix that represents a system of linear equations (in variables x,y,and z)has been reduced using Gauss-Jordan elimination.Write the solution represented by the augmented matrix. 
A)x = 0,y = 0,z = 0
B)x = 2x,y = 4y,z = 3z
C)x = 2,y = 3,z = 4
D)x = -2,y = -3,z = -4
E)x = 2,y = 0,z = 0
A)x = 0,y = 0,z = 0
B)x = 2x,y = 4y,z = 3z
C)x = 2,y = 3,z = 4
D)x = -2,y = -3,z = -4
E)x = 2,y = 0,z = 0
Question
Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix
New Row-Equivalent Matrix
A)Add -2 times R1 to R2.
B)Add 2 times R2 to R1.
C)Add 2 times R1 to R2.
D)Add -2 times R1 to R1.
E)Add -2 times R2 to R1.
New Row-Equivalent Matrix
A)Add -2 times R1 to R2.
B)Add 2 times R2 to R1.
C)Add 2 times R1 to R2.
D)Add -2 times R1 to R1.
E)Add -2 times R2 to R1.
Question
Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) 
A)x = 35,y = -3,z = 1
B)x = 4,y = 1,z = 5
C)x = 1,y = -4,z = -5
D)x = 1,y = 4,z = 5
E)x = -4,y = 5,z = -1
A)x = 35,y = -3,z = 1
B)x = 4,y = 1,z = 5
C)x = 1,y = -4,z = -5
D)x = 1,y = 4,z = 5
E)x = -4,y = 5,z = -1
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)x = 4,y = -2
B)x = -4,y = 2
C)x = 2,y = -4
D)x = 2,y = 4
E)no solution
A)x = 4,y = -2
B)x = -4,y = 2
C)x = 2,y = -4
D)x = 2,y = 4
E)no solution
Question
Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) 
A)x = 4,y = 2,z = -3
B)x = 3,y = -4,z = 2
C)x = 3,y = 4,z = -2
D)x = -18,y = -1,z = 4
E)x = -4,y = 3,z = 2
A)x = 4,y = 2,z = -3
B)x = 3,y = -4,z = 2
C)x = 3,y = 4,z = -2
D)x = -18,y = -1,z = 4
E)x = -4,y = 3,z = 2
Question
Fill in the blank using elementary row operations to form a row-equivalent matrix. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 
A)x = -3,y = -4
B)x = 4,y = 3
C)x = -4,y = -3
D)x = -3,y = 4
E)no solution
A)x = -3,y = -4
B)x = 4,y = 3
C)x = -4,y = -3
D)x = -3,y = 4
E)no solution
Question
Write the matrix in reduced row-echelon form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. 
A)x = 6,y = 3,z = -1
B)x = -6,y = -3,z = -1
C)x = 3,y = -1,z = -6
D)The systems yield different solutions.
E)x = -3,y = -1,z = -6
A)x = 6,y = 3,z = -1
B)x = -6,y = -3,z = -1
C)x = 3,y = -1,z = -6
D)The systems yield different solutions.
E)x = -3,y = -1,z = -6
Question
The currents in an electrical network are given by the solutions of the system 
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.
A)no solution
B)I1 = 3,I2 = 3,I3 = 7
C)I1 = 5,I2 = 4,I3 = 9
D)I1 = 3,I2 = 3,I3 = 6
E)I1 = 5,I2 = 9,I3 = 4
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.A)no solution
B)I1 = 3,I2 = 3,I3 = 7
C)I1 = 5,I2 = 4,I3 = 9
D)I1 = 3,I2 = 3,I3 = 6
E)I1 = 5,I2 = 9,I3 = 4
Question
The currents in an electrical network are given by the solutions of the system 
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 2,I2 = 3,I3 = 1
B)I1 = 2,I2 = 1,I3 = 3
C)I1 = 4,I2 = 4,I3 = 9
D)I1 = 4,I2 = 4,I3 = 8
E)no solution
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.A)I1 = 2,I2 = 3,I3 = 1
B)I1 = 2,I2 = 1,I3 = 3
C)I1 = 4,I2 = 4,I3 = 9
D)I1 = 4,I2 = 4,I3 = 8
E)no solution
Question
Solve the system using Gauss-Jordan elimination. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the system by Gauss - Jordan elimination. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the system using Gauss-Jordan elimination. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the system using Gaussian elimination. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 47: Matrices and Systems of Equations
1
Select the order for the following matrix.
A)2 × 2
B)4 × 4
C)3 × 1
D)4 × 1
E)1 × 4
A)2 × 2
B)4 × 4
C)3 × 1
D)4 × 1
E)1 × 4
1 × 4
2
Select the augmented matrix for the system of linear equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Select the system of linear equations represented by the following augmented matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. )
A) (-14,-5)
B) (-14,-5)
C) (-14,5)
D) (-5,-14)
E) (-5,-14)
A)
(-14,-5)
B)
(-14,-5)
C)
(-14,5)D)
(-5,-14)E)
(-5,-14) Unlock Deck
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7
Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix
A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.
Original Matrix New Row-Equivalent Matrix
A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.
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8
Select the augmented matrix for the system of linear equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Select the system of linear equations represented by the following augmented matrix.(Variables x,y,z,and w are used whenever applicable. )
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Select the order for the following matrix.
A)4 × 3
B)4 × 2
C)4 × 4
D)3 × 3
E)3 × 4
A)4 × 3
B)4 × 2
C)4 × 4
D)3 × 3
E)3 × 4
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11
Select the order for the following matrix.
A)2 × 3
B)3 × 1
C)3 × 2
D)3 × 3
E)2 × 2
A)2 × 3
B)3 × 1
C)3 × 2
D)3 × 3
E)2 × 2
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12
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. )
A) (7,0)
B) (-1,7)
C) (7,-1)
D) (7,1)
E) (7,1)
A)
(7,0)B)
(-1,7)C)
(7,-1)D)
(7,1)E)
(7,1) Unlock Deck
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13
Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix
A)Add 6 times Row 2 to Row 1.
B)Add 3 times Row 1 to Row 2.
C)Add 6 times Row 1 to Row 2.
D)Add 4 times Row 2 to Row 1.
E)Add 3 times Row 2 to Row 1.
Original Matrix New Row-Equivalent Matrix
A)Add 6 times Row 2 to Row 1.
B)Add 3 times Row 1 to Row 2.
C)Add 6 times Row 1 to Row 2.
D)Add 4 times Row 2 to Row 1.
E)Add 3 times Row 2 to Row 1.
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14
Determine whether the following matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form.
A)Row-echelon form
B)Not in row-echelon form
C)Reduced row-echelon form
A)Row-echelon form
B)Not in row-echelon form
C)Reduced row-echelon form
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15
Select the system of linear equations represented by the following augmented matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z and if applicable. )
A) (56,12,-6)
B) (44,0,-6)
C) (-40,12,6)
D) (44,0,-6)
E) (-40,12,6)
A)
(56,12,-6)B)
(44,0,-6)C)
(-40,12,6)D)
(44,0,-6)E)
(-40,12,6) Unlock Deck
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17
Select the augmented matrix for the system of linear equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Perform the sequence of row operations on the following matrix. Add -3 times R1 to R2.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Perform the sequence of row operations on the following matrix. Add R3 to R4.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Fill in the blank(s)using elementary row operations to form a row-equivalent matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix.
A)(-6,7)
B)(-6,5)
C)(-5,6)
D)(5,-6)
E)(6,5)
A)(-6,7)
B)(-6,5)
C)(-5,6)
D)(5,-6)
E)(6,5)
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22
Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form.
A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
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23
Determine the order of the matrix.
A)1 × 1
B)3
C)3 × 3
D)3 × 1
E)1 × 3
A)1 × 1
B)3
C)3 × 3
D)3 × 1
E)1 × 3
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24
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(-5,-5,4)
B)(5,-5,-4)
C)(-5,-5,-4)
D)(5,5,4)
E)(5,-5,4)
A)(-5,-5,4)
B)(5,-5,-4)
C)(-5,-5,-4)
D)(5,5,4)
E)(5,-5,4)
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25
Write the augmented matrix for the system of linear equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
The currents in an electrical network are given by the solution of the system where I1,I2 and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 5,I2 = 4,I3 = 8
B)I1 = 4,I2 = 4,I3 = 8
C)I1 = 3,I2 = 4,I3 = 8
D)I1 = 2,I2 = 4,I3 = 8
E)I1 = 1,I2 = 4,I3 = 8
where I1,I2 and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 5,I2 = 4,I3 = 8
B)I1 = 4,I2 = 4,I3 = 8
C)I1 = 3,I2 = 4,I3 = 8
D)I1 = 2,I2 = 4,I3 = 8
E)I1 = 1,I2 = 4,I3 = 8
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27
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix.
A)(0,8,-6)
B)(8,0,-6)
C)(8,-6,0)
D)(-8,-6,0)
E)(8,6,0)
A)(0,8,-6)
B)(8,0,-6)
C)(8,-6,0)
D)(-8,-6,0)
E)(8,6,0)
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28
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)
A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)
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29
Write the matrix in reduced row-echelon form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(10,1)
B)(2,1)
C)(2,-6)
D)(-2,1)
E)(2,-1)
A)(10,1)
B)(2,1)
C)(2,-6)
D)(-2,1)
E)(2,-1)
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31
Fill in the blank using elementary row operations to form a row-equivalent matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix.
A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)
A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)
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33
Use matrices to find the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(3,4)
B)(-3,4)
C)(5,18)
D)(-3,-4)
E)(3,-4)
A)(3,4)
B)(-3,4)
C)(5,18)
D)(-3,-4)
E)(3,-4)
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34
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)
A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)
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35
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)
A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)
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36
Determine the order of the matrix.
A)3 × 3
B)2 × 2
C)3 × 1
D)2 × 3
E)3 × 2
A)3 × 3
B)2 × 2
C)3 × 1
D)2 × 3
E)3 × 2
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37
Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix
New Row-Equivalent Matrix
A)Add 2 times R1 to R2.
B)Add -2 times R1 to R2.
C)Add 2 times R2 to R1.
D)Add -2 times R2 to R1.
E)Add 2 times R1 to R1.
New Row-Equivalent Matrix
A)Add 2 times R1 to R2.
B)Add -2 times R1 to R2.
C)Add 2 times R2 to R1.
D)Add -2 times R2 to R1.
E)Add 2 times R1 to R1.
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38
Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system.
A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)
A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)
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39
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)(1,4)
B)(3,4)
C)(1,12)
D)(4,1)
E)(12,4)
A)(1,4)
B)(3,4)
C)(1,12)
D)(4,1)
E)(12,4)
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40
Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. )
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form.
A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
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42
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)x = 5,y = -1,z = -6
B)x = -5,y = -1,z = -6
C)x = -5,y = 1,z = -6
D)x = 1,y = 5,z = 6
E)no solution
A)x = 5,y = -1,z = -6
B)x = -5,y = -1,z = -6
C)x = -5,y = 1,z = -6
D)x = 1,y = 5,z = 6
E)no solution
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43
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)x = 5,y = -2,z = 4
B)x = 2,y = 5,z = -4
C)x = -5,y = -2,z = 4
D)no solution
E)x = -5,y = 2,z = 4
A)x = 5,y = -2,z = 4
B)x = 2,y = 5,z = -4
C)x = -5,y = -2,z = 4
D)no solution
E)x = -5,y = 2,z = 4
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44
Use a system of equations to find the specified equation that passes through the points.Solve the system using matrices. Parabola: y = ax2 + bx + c
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
45
Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. )
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Perform the sequence of row operations on the matrix.What did the operations accomplish? Add -4 times R1 to R2,
Add -1 times R1 to R3,
Add -2 times R2 to R3,
Add -1 times R2 to R1.
A) The operations produce a row-equivalent matrix in reduced row-echelon form.
B) The operations produce a row-equivalent matrix in reduced row-echelon form.
C) The operations produce a row-equivalent matrix in reduced row-echelon form.
D) The operations produce a row-equivalent matrix in reduced row-echelon form.
E) The operations produce a row-equivalent matrix in reduced row-echelon form.
Add -4 times R1 to R2,Add -1 times R1 to R3,
Add -2 times R2 to R3,
Add -1 times R2 to R1.
A)
The operations produce a row-equivalent matrix in reduced row-echelon form.B)
The operations produce a row-equivalent matrix in reduced row-echelon form.C)
The operations produce a row-equivalent matrix in reduced row-echelon form.D)
The operations produce a row-equivalent matrix in reduced row-echelon form.E)
The operations produce a row-equivalent matrix in reduced row-echelon form. Unlock Deck
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47
Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices.
A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3
A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3
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48
Write the augmented matrix for the system of linear equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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49
Write the matrix in reduced row-echelon form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Determine the order of the matrix.
A)2 × 3
B)3 × 3
C)3 × 1
D)3 × 2
E)2 × 2
A)2 × 3
B)3 × 3
C)3 × 1
D)3 × 2
E)2 × 2
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51
An augmented matrix that represents a system of linear equations (in variables x,y,and z)has been reduced using Gauss-Jordan elimination.Write the solution represented by the augmented matrix.
A)x = 0,y = 0,z = 0
B)x = 2x,y = 4y,z = 3z
C)x = 2,y = 3,z = 4
D)x = -2,y = -3,z = -4
E)x = 2,y = 0,z = 0
A)x = 0,y = 0,z = 0
B)x = 2x,y = 4y,z = 3z
C)x = 2,y = 3,z = 4
D)x = -2,y = -3,z = -4
E)x = 2,y = 0,z = 0
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52
Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix
New Row-Equivalent Matrix
A)Add -2 times R1 to R2.
B)Add 2 times R2 to R1.
C)Add 2 times R1 to R2.
D)Add -2 times R1 to R1.
E)Add -2 times R2 to R1.
New Row-Equivalent Matrix
A)Add -2 times R1 to R2.
B)Add 2 times R2 to R1.
C)Add 2 times R1 to R2.
D)Add -2 times R1 to R1.
E)Add -2 times R2 to R1.
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53
Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. )
A)x = 35,y = -3,z = 1
B)x = 4,y = 1,z = 5
C)x = 1,y = -4,z = -5
D)x = 1,y = 4,z = 5
E)x = -4,y = 5,z = -1
A)x = 35,y = -3,z = 1
B)x = 4,y = 1,z = 5
C)x = 1,y = -4,z = -5
D)x = 1,y = 4,z = 5
E)x = -4,y = 5,z = -1
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54
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)x = 4,y = -2
B)x = -4,y = 2
C)x = 2,y = -4
D)x = 2,y = 4
E)no solution
A)x = 4,y = -2
B)x = -4,y = 2
C)x = 2,y = -4
D)x = 2,y = 4
E)no solution
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55
Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. )
A)x = 4,y = 2,z = -3
B)x = 3,y = -4,z = 2
C)x = 3,y = 4,z = -2
D)x = -18,y = -1,z = 4
E)x = -4,y = 3,z = 2
A)x = 4,y = 2,z = -3
B)x = 3,y = -4,z = 2
C)x = 3,y = 4,z = -2
D)x = -18,y = -1,z = 4
E)x = -4,y = 3,z = 2
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56
Fill in the blank using elementary row operations to form a row-equivalent matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
A)x = -3,y = -4
B)x = 4,y = 3
C)x = -4,y = -3
D)x = -3,y = 4
E)no solution
A)x = -3,y = -4
B)x = 4,y = 3
C)x = -4,y = -3
D)x = -3,y = 4
E)no solution
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58
Write the matrix in reduced row-echelon form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices.
A)x = 6,y = 3,z = -1
B)x = -6,y = -3,z = -1
C)x = 3,y = -1,z = -6
D)The systems yield different solutions.
E)x = -3,y = -1,z = -6
A)x = 6,y = 3,z = -1
B)x = -6,y = -3,z = -1
C)x = 3,y = -1,z = -6
D)The systems yield different solutions.
E)x = -3,y = -1,z = -6
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60
The currents in an electrical network are given by the solutions of the system where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.
A)no solution
B)I1 = 3,I2 = 3,I3 = 7
C)I1 = 5,I2 = 4,I3 = 9
D)I1 = 3,I2 = 3,I3 = 6
E)I1 = 5,I2 = 9,I3 = 4
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.A)no solution
B)I1 = 3,I2 = 3,I3 = 7
C)I1 = 5,I2 = 4,I3 = 9
D)I1 = 3,I2 = 3,I3 = 6
E)I1 = 5,I2 = 9,I3 = 4
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61
The currents in an electrical network are given by the solutions of the system where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.
A)I1 = 2,I2 = 3,I3 = 1
B)I1 = 2,I2 = 1,I3 = 3
C)I1 = 4,I2 = 4,I3 = 9
D)I1 = 4,I2 = 4,I3 = 8
E)no solution
where I1,I2,and I3 are measured in amperes.Solve the system of equations using matrices.A)I1 = 2,I2 = 3,I3 = 1
B)I1 = 2,I2 = 1,I3 = 3
C)I1 = 4,I2 = 4,I3 = 9
D)I1 = 4,I2 = 4,I3 = 8
E)no solution
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62
Solve the system using Gauss-Jordan elimination.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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63
Solve the system by Gauss - Jordan elimination.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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64
Solve the system using Gauss-Jordan elimination.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Solve the system using Gaussian elimination.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 65 flashcards in this deck.
