Perform the indicated row operations, then write the new matrix. -\[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ - 2 & 3 & 5 & 3 \\ 3 & 2 & 4 & 1 \end{array} \right] \begin{array} { c } 2 R 1 + R 2 \rightarrow R 2 , \\ - 3 R 1 + R 3 \rightarrow R 3 \end{array}\]

A) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 1 \\ 0 & - 1 & 1 & 4 \end{array} \right]\] B) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 3 \\ 0 & - 1 & 1 & 1 \end{array} \right]\] C) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ - 2 & 3 & 5 & 3 \\ 0 & - 1 & 1 & 1 \end{array} \right]\] D) $\left[ \begin{array} { l l l | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 1 \\ 3 & 2 & 4 & 1 \end{array} \right]$ A) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 1 \\ 0 & - 1 & 1 & 4 \end{array} \right]\] B) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 3 \\ 0 & - 1 & 1 & 1 \end{array} \right]\] C) \[\left[ \begin{array} { r r r | r } 1 & 1 & 1 & - 1 \\ - 2 & 3 & 5 & 3 \\ 0 & - 1 & 1 & 1 \end{array} \right]\] D) $\left[ \begin{array} { l l l | r } 1 & 1 & 1 & - 1 \\ 0 & 5 & 7 & 1 \\ 3 & 2 & 4 & 1 \end{array} \right]$

Find the cofactor of the given element. -\[\begin{array} { l } a _ { 13 } \\ A = \left[ a _ { i j } \right] = \left[ \begin{array} { r r r } 7 & - 2 & 5 \\ 2 & 5 & 4 \\ - 1 & - 9 & 3 \end{array} \right] \end{array}\]

A) $- 8$ B) $- 18$ C) 13 D) $- 13$ A) $- 8$ B) $- 18$ C) 13 D) $- 13$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. -\[\begin{array} { l } 2 ( x - 2 z ) = 3 y + x + 30 \\ x = 2 y - 2 z - 3 \\ - 5 x + 2 y + 6 z = - 41 \end{array}\]

A) $\{ ( 3 , - 1,5 ) \}$ B) $\{ ( 1 , - 3 , - 5 ) \}$ C) $\{ ( - 3,1 , - 5 ) \}$ D) $\{ ( - 1,3,5 ) \}$ A) $\{ ( 3 , - 1,5 ) \}$ B) $\{ ( 1 , - 3 , - 5 ) \}$ C) $\{ ( - 3,1 , - 5 ) \}$ D) $\{ ( - 1,3,5 ) \}$

Solve the problem. -A gas station manager records the number of gallons of Regular, Plus, and Premium gasoline sold during the week (Monday-Friday) and on the weekends (Saturday-Sunday) in matrix A. The selling Price and profit for 1 gal of each type of gasoline is given in matrix B. $\quad $$\quad $$\text { Regular}$$\quad $ $\text { Plus}$ $\text { Premium }$ $A=\left[\begin{array}{rrr} 4,270 & 1,760 & 810 \\ 2,320 & 610 & 410 \end{array}\right] \begin{array}{l} \text { Weekdays } \\ \text { Weekend } \end{array}$ \[\begin{array}{l} \text { Selling }\\ B = \left[ \begin{array} { l l } \text { Price } & \text { Profit } \\ \$ 3.49 & \$ 0.26 \\ \$ 4.09 & \$ 0.28 \\ \$ 0.20 \end{array} \right] \text { Regular } \text { Plus } \text { Premium } \end{array}\] a. Compute $A B$. b. Determine the profit for the weekend. c. Determine the revenue for the entire week.

A) a. $A B = \left[ \begin{array} { l r } \$ 24,709.60 & \$ 12,024.60 \\ \$ 1,765.00 & \$ 856.00 \end{array} \right]$ b. $\$ 856.00$ c. $\$ 26,474.60$ B) a. $A B = \left[ \begin{array} { r r } \$ 24,709.60 & \$ 1,765.00 \\ \$ 12,024.60 & \$ 856.00 \end{array} \right]$ b. $\$ 2,621.00$ c. $\$ 12,024.60$ C) a. $A B = \left[ \begin{array} { r r } \$ 24,709.60 & \$ 1,765.00 \\ \$ 12,024.60 & \$ 856.00 \end{array} \right]$ b. $\$ 856.00$ c. $\$ 36,734.20$ D) a. $A B = \left[ \begin{array} { l r } \$ 24,709.60 & \$ 12,024.60 \\ \$ 1,765.00 & \$ 856.00 \end{array} \right]$ b. $\$ 12,880.60$ c. $\$ 1,765.00$ A) a. $A B = \left[ \begin{array} { l r } \$ 24,709.60 & \$ 12,024.60 \\ \$ 1,765.00 & \$ 856.00 \end{array} \right]$ b. $\$ 856.00$ c. $\$ 26,474.60$ B) a. $A B = \left[ \begin{array} { r r } \$ 24,709.60 & \$ 1,765.00 \\ \$ 12,024.60 & \$ 856.00 \end{array} \right]$ b. $\$ 2,621.00$ c. $\$ 12,024.60$ C) a. $A B = \left[ \begin{array} { r r } \$ 24,709.60 & \$ 1,765.00 \\ \$ 12,024.60 & \$ 856.00 \end{array} \right]$ b. $\$ 856.00$ c. $\$ 36,734.20$ D) a. $A B = \left[ \begin{array} { l r } \$ 24,709.60 & \$ 12,024.60 \\ \$ 1,765.00 & \$ 856.00 \end{array} \right]$ b. $\$ 12,880.60$ c. $\$ 1,765.00$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. -\[\begin{array} { l } - 6 x + 15 y = 15 \\ 2 x - 5 y = - 5 \end{array}\]

A) $\{ ( 15 , - 5 ) \}$ B) $\left\{ \left( \frac { 5 } { 2 } x - \frac { 5 } { 2 } , y \right) \mid y \right.$ is any real number C) $\{ ( - 9 , - 5 ) \}$ D) {} A) $\{ ( 15 , - 5 ) \}$ B) $\left\{ \left( \frac { 5 } { 2 } x - \frac { 5 } { 2 } , y \right) \mid y \right.$ is any real number C) $\{ ( - 9 , - 5 ) \}$ D) {}

Exam 6: Matrices and Determinants and Applications

Physicists know that if each edge of a thin conducting plate is kept at a constant temperature, then the temperature at the interior points is the mean (average) of the four surrounding points equidistant from the interior point. Use this principle in to find the temperature at points $x _ { 1 } , x _ { 2 } , x _ { 3 } , \text { and } x _ { 4 }$ - $Physicists know that if each edge of a thin conducting plate is kept at a constant temperature, then the temperature at the interior points is the mean (average) of the four surrounding points equidistant from the interior point. Use this principle in to find the temperature at points x _ { 1 } , x _ { 2 } , x _ { 3 } , \text { and } x _ { 4 } -$

(Multiple Choice)

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Question 61

Perform the indicated row operations, then write the new matrix. - open bracket 1 1 1 -1 -2 3 5 3 3 2 4 1 close bracket 2R1+R2\rightarrowR2, -3R1+R3\rightarrowR3

(Multiple Choice)

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Question 62

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A matrix that does not have an inverse is called a matrix. A matrix that does have an inverse is said to be invertible or .

(Short Answer)

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Question 63

Find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A, B, and C. - $\frac { - 3 x ^ { 2 } + 7 x - 10 } { ( x + 2 ) ( x - 1 ) ^ { 2 } } = \frac { A } { x + 2 } + \frac { B } { x - 1 } - \frac { C } { ( x - 1 ) ^ { 2 } }$

(Multiple Choice)

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Question 64

Find the cofactor of the given element. - A= = 7 -2 5 2 5 4 -1 -9 3

(Multiple Choice)

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Question 65

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 2(x-2z)=3y+x+30 x=2y-2z-3 -5x+2y+6z=-41

(Multiple Choice)

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Question 66

Solve the problem. -A gas station manager records the number of gallons of Regular, Plus, and Premium gasoline sold during the week (Monday-Friday) and on the weekends (Saturday-Sunday) in matrix A. The selling Price and profit for 1 gal of each type of gasoline is given in matrix B. $\quad$ $\quad$ $\text { Regular}$ $\quad$ $\text { Plus}$ $\text { Premium }$ Aequals open bracket 4,270 1,760 810 2,320 610 410 close bracket Weekdays Weekend Selling B= Price Profit \ 3.49 \ 0.26 \ 4.09 \ 0.28 \ 0.20 Regular Plus Premium a. Compute $A B$ . b. Determine the profit for the weekend. c. Determine the revenue for the entire week.

(Multiple Choice)

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Question 67

An________ matrix is used to represent a system of linear equations written in standard form.

(Short Answer)

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Question 68

Determine whether A and B are inverses. - $A = \left[ \begin{array} { r r r } - 2 & - 1 & - 5 \\2 & - 1 & 3 \\1 & 4 & - 2\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } \frac { 5 } { 16 } & \frac { 11 } { 16 } & \frac { 1 } { 4 } \\- \frac { 7 } { 32 } & - \frac { 9 } { 32 } & \frac { 1 } { 8 } \\- \frac { 9 } { 32 } & - \frac { 7 } { 32 } & - \frac { 1 } { 8 }\end{array} \right]$

(Multiple Choice)

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Question 69

Find the indicated matrix. -Find $- 3 ( A - B )$ $A = \left[ \begin{array} { r r r } 1 & 9 & - 7 \\ - 9 & 4 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 2 & 8 & 2 \\ 8 & 4 & - 9 \end{array} \right]$

(Multiple Choice)

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Question 70

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { c c } \frac { 5 } { 2 } & \frac { 3 } { 4 } \\20 & 4\end{array} \right]$

(Multiple Choice)

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Question 71

Choose the one alternative that best completes the statement or answers the question. For the given augmented matrix, determine the number of solutions to the corresponding system of equations. - $\left[ \begin{array} { l l l | r } 1 & 0 & 0 & - 3 \\0 & 1 & 0 & - 9 \\0 & 0 & 1 & 0\end{array} \right]$

(Multiple Choice)

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Question 72

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When applying Cramer's rule, if D = 0, then the system (does / does not) have a unique solution.

(Short Answer)

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Question 73

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { l l l l } 3 & 8 & - 5 & - 5\end{array} \right]$

(Multiple Choice)

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Question 74

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - -3x-6y+9z =12 -x+2y =-10 x-8z =-2

(Multiple Choice)

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Question 75

Write the word or phrase that best completes each statement or answers the question. Solve the problem. - $Write the word or phrase that best completes each statement or answers the question. Solve the problem. - a. Assume that traffic flows at a rate of 215 vehicles per hour on the stretch of road between intersections \mathrm { D } and \mathrm { A } . Find the flow rates x _ { 1 } , x _ { 2 } , and x _ { 3 } . b. If traffic flows at a rate of between 195 and 270 vehicles per hour inclusive between intersections \mathrm { D } and \mathrm { A } , find the flow rates x _ { 1 } , x _ { 2 } , and x _ { 3 } .$ a. Assume that traffic flows at a rate of 215 vehicles per hour on the stretch of road between intersections $\mathrm { D }$ and $\mathrm { A }$ . Find the flow rates $x _ { 1 } , x _ { 2 }$ , and $x _ { 3 }$ . b. If traffic flows at a rate of between 195 and 270 vehicles per hour inclusive between intersections $\mathrm { D }$ and $\mathrm { A }$ , find the flow rates $x _ { 1 } , x _ { 2 }$ , and $x _ { 3 }$ .

(Multiple Choice)

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Question 76

Find AB and BA. - $A = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 1 & 1 & - 5 \\ 8 & - 9 & - 5 \\ - 1 & 4 & 5 \end{array} \right]$

(Multiple Choice)

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Question 77

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -6x+15y=15 2x-5y=-5

(Multiple Choice)

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Question 78

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { r r } - 5 & - 4 \\- 25 & - 20\end{array} \right]$

(Multiple Choice)

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Question 79

Perform the indicated operations. -Find 2A $A = \left[ \begin{array} { c c c } - 2 & 0 & 3 \\ - 1 & \sqrt { 3 } & \frac { 3 } { 2 } \end{array} \right]$

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Question 80

Showing 61 - 80 of 154

Perform the indicated row operations, then write the new matrix. - open bracket 1 1 1 -1 -2 3 5 3 3 2 4 1 close bracket 2R1+R2\rightarrowR2, -3R1+R3\rightarrowR3

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A matrix that does not have an inverse is called a matrix. A matrix that does have an inverse is said to be invertible or .

Find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A, B, and C. - $\frac { - 3 x ^ { 2 } + 7 x - 10 } { ( x + 2 ) ( x - 1 ) ^ { 2 } } = \frac { A } { x + 2 } + \frac { B } { x - 1 } - \frac { C } { ( x - 1 ) ^ { 2 } }$

Find the cofactor of the given element. - A= = 7 -2 5 2 5 4 -1 -9 3

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 2(x-2z)=3y+x+30 x=2y-2z-3 -5x+2y+6z=-41

An________ matrix is used to represent a system of linear equations written in standard form.

Find the indicated matrix. -Find $- 3 ( A - B )$ $A = \left[ \begin{array} { r r r } 1 & 9 & - 7 \\ - 9 & 4 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 2 & 8 & 2 \\ 8 & 4 & - 9 \end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { c c } \frac { 5 } { 2 } & \frac { 3 } { 4 } \\20 & 4\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When applying Cramer's rule, if D = 0, then the system (does / does not) have a unique solution.

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { l l l l } 3 & 8 & - 5 & - 5\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - -3x-6y+9z =12 -x+2y =-10 x-8z =-2

Find AB and BA. - $A = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 1 & 1 & - 5 \\ 8 & - 9 & - 5 \\ - 1 & 4 & 5 \end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -6x+15y=15 2x-5y=-5

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { r r } - 5 & - 4 \\- 25 & - 20\end{array} \right]$

Perform the indicated operations. -Find 2A $A = \left[ \begin{array} { c c c } - 2 & 0 & 3 \\ - 1 & \sqrt { 3 } & \frac { 3 } { 2 } \end{array} \right]$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 6: Matrices and Determinants and Applications

Perform the indicated row operations, then write the new matrix. - open bracket 1 1 1 -1 -2 3 5 3 3 2 4 1 close bracket 2R1+R2\rightarrowR2, -3R1+R3\rightarrowR3

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A matrix that does not have an inverse is called a ________matrix. A matrix that does have an inverse is said to be invertible or ________.

Find the cofactor of the given element. - A= = 7 -2 5 2 5 4 -1 -9 3

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 2(x-2z)=3y+x+30 x=2y-2z-3 -5x+2y+6z=-41

An________ matrix is used to represent a system of linear equations written in standard form.

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - A=[5234204]A = \left[ \begin{array} { c c } \frac { 5 } { 2 } & \frac { 3 } { 4 } \\20 & 4\end{array} \right]A=[25​20​43​4​]

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When applying Cramer's rule, if D = 0, then the system (does / does not) have a unique solution.

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - [38−5−5]\left[ \begin{array} { l l l l } 3 & 8 & - 5 & - 5\end{array} \right][3​8​−5​−5​]

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - -3x-6y+9z =12 -x+2y =-10 x-8z =-2

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -6x+15y=15 2x-5y=-5

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - A=[−5−4−25−20]A = \left[ \begin{array} { r r } - 5 & - 4 \\- 25 & - 20\end{array} \right]A=[−5−25​−4−20​]

Perform the indicated operations. -Find 2A A=[−203−1332]A = \left[ \begin{array} { c c c } - 2 & 0 & 3 \\ - 1 & \sqrt { 3 } & \frac { 3 } { 2 } \end{array} \right]A=[−2−1​03​​323​​]

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A matrix that does not have an inverse is called a matrix. A matrix that does have an inverse is said to be invertible or .

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { c c } \frac { 5 } { 2 } & \frac { 3 } { 4 } \\20 & 4\end{array} \right]$

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { l l l l } 3 & 8 & - 5 & - 5\end{array} \right]$

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { r r } - 5 & - 4 \\- 25 & - 20\end{array} \right]$

Perform the indicated operations. -Find 2A $A = \left[ \begin{array} { c c c } - 2 & 0 & 3 \\ - 1 & \sqrt { 3 } & \frac { 3 } { 2 } \end{array} \right]$