Question 1

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x, y, and z.)

Accepted Answer

A)  x = -8, y = 1, z = -1 
B)  x = -2, y = -4, z = -5 
C)  x = -4, y = 2, z = 5 
D)  x = -4, y = -2, z = -5 
E)  x = 2, y = -5, z = 4 
A)  x = -8, y = 1, z = -1 
B)  x = -2, y = -4, z = -5 
C)  x = -4, y = 2, z = 5 
D)  x = -4, y = -2, z = -5 
E)  x = 2, y = -5, z = 4 D

Question 2

Find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    C

Question 3

Find all (a) minors and (b) cofactors of the matrix   Show your work.

Accepted Answer

(a)   (b)

Question 4

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Find which of the following matrices is an inverse to the matrix A below if any.   Matrix I :   Matrix II :   Matrix III :

Accepted Answer

A)  Each of the matrices I and III is an inverse of A. 
B)  Each of the matrices I and II is an inverse of A. 
C)  Each of the matrices II and III is an inverse of A. 
D)  Matrix II is an inverse of A. 
E)  None of the matrices is an inverse of A. 
A)  Each of the matrices I and III is an inverse of A. 
B)  Each of the matrices I and II is an inverse of A. 
C)  Each of the matrices II and III is an inverse of A. 
D)  Matrix II is an inverse of A. 
E)  None of the matrices is an inverse of A.

Question 7

Given matrix   Find   the inverse matrix.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Given   and   , find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Find the determinant of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Find A2.(Note: A2 = AA.)

Accepted Answer

A)    
B)    
C)    
D)    
E)  not possible 
A)    
B)    
C)    
D)    
E)  not possible

Question 11

Solve the system of equations below by the Gaussian elimination method:

Accepted Answer

A)    
B)    
C)    
D)    
E)  no solution 
A)    
B)    
C)    
D)    
E)  no solution

Question 12

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix   Show all your work.

Accepted Answer

The answer of Find the uncoded 1 × 3 row...

Question 13

The area of a triangle with vertices     and   can be given as the absolute value of the determinant   Use this formula to find the area of each triangle whose coordinates are     and

Accepted Answer

A)  4.5 
B)  1.0 
C)  19.0 
D)  5.0 
E)  17.0 
A)  4.5 
B)  1.0 
C)  19.0 
D)  5.0 
E)  17.0

Question 14

Write the matrix in reduced row-echelon form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix   Show all your work.

Accepted Answer

The answer of Find the uncoded 1 × 3 row...

Question 16

Write the system of linear equations represented by the augmented matrix.(Use variables x, y, z, and w.)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find the inverse of the given matrix.

Accepted Answer

A)    
B)    
C)    
D)    
E)  The matrix does not have an inverse. 
A)    
B)    
C)    
D)    
E)  The matrix does not have an inverse.

Question 18

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.

Accepted Answer

A)  x = 8, y = 1, z = 5 
B)  x = -8, y = -1, z = -5 
C)  x = 0, y = 0, z = 0 
D)  x = 8x, y = 5y, z = z 
E)  x = 8, y = 0, z = 0 
A)  x = 8, y = 1, z = 5 
B)  x = -8, y = -1, z = -5 
C)  x = 0, y = 0, z = 0 
D)  x = 8x, y = 5y, z = z 
E)  x = 8, y = 0, z = 0

Question 19

Find x and y.

Accepted Answer

A)  x = 2, y = 4 
B)  x = 2, y = 3 
C)  x = 3, y = 3 
D)  x = 4, y = 3 
E)  no solution 
A)  x = 2, y = 4 
B)  x = 2, y = 3 
C)  x = 3, y = 3 
D)  x = 4, y = 3 
E)  no solution

Question 20

Determine a positive value for y such that a triangle with vertices   , and   has an area of   square units.

Accepted Answer

A)  8 
B)  6 
C)  9 
D)  11 
E)  1 
A)  8 
B)  6 
C)  9 
D)  11 
E)  1

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x, y, and z.)

Find

Find all (a) minors and (b) cofactors of the matrix Show your work.

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Find which of the following matrices is an inverse to the matrix A below if any. Matrix I : Matrix II : Matrix III :

Given matrix Find the inverse matrix.

Given and , find

Find the determinant of

Find A².(Note: A² = AA.)

Solve the system of equations below by the Gaussian elimination method:

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix Show all your work.

The area of a triangle with vertices and can be given as the absolute value of the determinant Use this formula to find the area of each triangle whose coordinates are and

Write the matrix in reduced row-echelon form.

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix Show all your work.

Write the system of linear equations represented by the augmented matrix.(Use variables x, y, z, and w.)

Find the inverse of the given matrix.

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.

Find x and y.

Determine a positive value for y such that a triangle with vertices , and has an area of square units.

Fundamental Concepts of Algebra

Equations and Inequalities

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Exam 6: Matrices and Determinants

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x, y, and z.)

Find

Find all (a) minors and (b) cofactors of the matrix Show your work.

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Use the matrix capabilities of a graphing utility to find the determinant of the matrix

Find which of the following matrices is an inverse to the matrix A below if any. Matrix I : Matrix II : Matrix III :

Given matrix Find the inverse matrix.

Given and , find

Find the determinant of

Find A2.(Note: A2 = AA.)

Solve the system of equations below by the Gaussian elimination method:

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix Show all your work.

The area of a triangle with vertices and can be given as the absolute value of the determinant Use this formula to find the area of each triangle whose coordinates are and

Write the matrix in reduced row-echelon form.

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND"; then encode the message using the encoding matrix Show all your work.

Write the system of linear equations represented by the augmented matrix.(Use variables x, y, z, and w.)

Find the inverse of the given matrix.

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.

Find x and y.

Determine a positive value for y such that a triangle with vertices , and has an area of square units.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Sequences, Series, and Probability

Filters

Find A².(Note: A² = AA.)