Use the Gauss-Jordan method to solve the system of equations. -$ \begin{array}{l} 8 x+9 y-z=48 \\ x-4 y+7 z=65 \\ 2 x+y+z=22 \end{array} $

A) $ (6,1,9) $ B) $ (6,9,1) $ C) $ (-6,1,12) $ D) No solution A) $ (6,1,9) $ B) $ (6,9,1) $ C) $ (-6,1,12) $ D) No solution

Solve the system of equations by using the inverse of the coefficient matrix. -\[ \begin{array}{l} x-y+z=-7 \\ x+y+z=1 \\ x+y-z=-1 \end{array} \]

A) $ (-4,1,4) $ B) $ (1,-4,4) $ C) $ (-4,4,1) $ D) No inverse, no solution for system A) $ (-4,1,4) $ B) $ (1,-4,4) $ C) $ (-4,4,1) $ D) No inverse, no solution for system

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place.\[ \begin{array}{l} 1.5 x-0.4 y+1.6 z=2.4 \\ 4.5 x-7.0 y-0.4 z=-4.0 \\ 3.8 x+2.4 y+2.0 z=8.6 \end{array} \]

A) $ (0.8,0.9,0.6) $ B) $ (1.1,1.2,0.8) $ C) $ (0.5,0.6,0.4) $ D) $ (0.3,0.3,0.2) $ A) $ (0.8,0.9,0.6) $ B) $ (1.1,1.2,0.8) $ C) $ (0.5,0.6,0.4) $ D) $ (0.3,0.3,0.2) $

Use the Gauss-Jordan method to solve the system of equations. -\[ \begin{array}{l} x+y+z=7 \\ x-y+2 z=7 \\ 2 x+3 z=14 \end{array} \]

A) $ \left(\frac{-3 z+14}{2}, \frac{z}{2}, z\right) $ B) $ \left(\frac{-3 z-14}{2}, \frac{z}{2}, z\right) $ C) $ \left(\frac{-3 z+14}{2}, 2 z, z\right) $ D) $ \left(\frac{3 z+14}{2}, \frac{z}{2}, z\right) $ A) $ \left(\frac{-3 z+14}{2}, \frac{z}{2}, z\right) $ B) $ \left(\frac{-3 z-14}{2}, \frac{z}{2}, z\right) $ C) $ \left(\frac{-3 z+14}{2}, 2 z, z\right) $ D) $ \left(\frac{3 z+14}{2}, \frac{z}{2}, z\right) $

Use the echelon method to solve the system of two equations in two unknowns. -\[ \begin{array}{l} 4 x-2 y=9 \\ 20 x-10 y=27 \end{array} \]

A) $ \left(\frac{1}{2} y+\frac{9}{4}, y\right) $ B) $ \left(1,-\frac{5}{2}\right) $ C) $ (1,0) $ D) No solution A) $ \left(\frac{1}{2} y+\frac{9}{4}, y\right) $ B) $ \left(1,-\frac{5}{2}\right) $ C) $ (1,0) $ D) No solution

Exam 2: Systems of Linear Equations and Matrices

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $\left[\begin{array}{rr}9 & -2 \\ 7 & -2\end{array}\right]$ and $\left[\begin{array}{rr}\frac{1}{2} & \frac{1}{2} \\ -\frac{7}{4} & -\frac{9}{4}\end{array}\right]$

(True/False)

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Question 41

Find the matrix product, if possible. - $\left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right]$

(Multiple Choice)

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Question 42

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ . $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$

(Multiple Choice)

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Question 43

Provide an appropriate response. -If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

(Multiple Choice)

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Question 44

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $\frac{1}{3} R_{1}+\frac{1}{2} R_{2}$ . $\left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right]$

(Multiple Choice)

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Question 45

Solve the problem. -Janet is planning to visit Arizona, New Mexico, and California on a 20-day vacation. If she plans to spend as much time in New Mexico as she does in the other two states combined, how can she allot her time in the three states? (Let $x$ denote the number of days in Arizona, $y$ the number of days in New Mexico, and $z$ the number of days in California. Let $z$ be the parameter.)

(Multiple Choice)

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Question 46

Use the Gauss-Jordan method to solve the system of equations. - 8x+9y-z=48 x-4y+7z=65 2x+y+z=22

(Multiple Choice)

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Question 47

The property does not apply to matrix multiplication.

(Short Answer)

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Question 48

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. What is The cost of 100 batches of each candy using ingredients from supplier Y?

(Multiple Choice)

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Question 49

Solve the system of equations by using the inverse of the coefficient matrix. - x-y+z=-7 x+y+z=1 x+y-z=-1

(Multiple Choice)

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Question 50

Find the value. -Let $\mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C}$

(Multiple Choice)

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Question 51

Find the inverse, if it exists, for the matrix. - $A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$

(Multiple Choice)

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Question 52

(Essay)

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Question 53

Perform the indicated operation, where possible. - $\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right]$

(Multiple Choice)

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Question 54

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. 1.5x-0.4y+1.6z=2.4 4.5x-7.0y-0.4z=-4.0 3.8x+2.4y+2.0z=8.6

(Multiple Choice)

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Question 55

-

(True/False)

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Question 56

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=7 x-y+2z=7 2x+3z=14

(Multiple Choice)

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Question 57

Use the echelon method to solve the system of two equations in two unknowns. - 4x-2y=9 20x-10y=27

(Multiple Choice)

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Question 58

Find the ratios of products A, B, and C using a closed model. -

(Multiple Choice)

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Question 59

Find the production matrix for the input-output and demand matrices using the open model. - $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$

(Multiple Choice)

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Question 60

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $\left[\begin{array}{rr}9 & -2 \\ 7 & -2\end{array}\right]$ and $\left[\begin{array}{rr}\frac{1}{2} & \frac{1}{2} \\ -\frac{7}{4} & -\frac{9}{4}\end{array}\right]$

Find the matrix product, if possible. - $\left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right]$

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ . $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$

Provide an appropriate response. -If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $\frac{1}{3} R_{1}+\frac{1}{2} R_{2}$ . $\left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - 8x+9y-z=48 x-4y+7z=65 2x+y+z=22

The property does not apply to matrix multiplication.

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. What is The cost of 100 batches of each candy using ingredients from supplier Y?

Solve the system of equations by using the inverse of the coefficient matrix. - x-y+z=-7 x+y+z=1 x+y-z=-1

Find the value. -Let $\mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C}$

Find the inverse, if it exists, for the matrix. - $A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$

Perform the indicated operation, where possible. - $\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right]$

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. 1.5x-0.4y+1.6z=2.4 4.5x-7.0y-0.4z=-4.0 3.8x+2.4y+2.0z=8.6

-

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=7 x-y+2z=7 2x+3z=14

Use the echelon method to solve the system of two equations in two unknowns. - 4x-2y=9 20x-10y=27

Find the ratios of products A, B, and C using a closed model. -

Find the production matrix for the input-output and demand matrices using the open model. - $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$

Linear Functions

Filters

Exam 2: Systems of Linear Equations and Matrices

Find the matrix product, if possible. - [3−2104−3][30−21] \left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right] [30​−24​1−3​][3−2​01​]

Use the indicated row operation to change the matrix. -Replace R2 R_{2} R2​ by R1+R2 R_{1}+R_{2} R1​+R2​ . [102−113] \left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right] [1−1​01​23​]

Provide an appropriate response. -If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

Use the indicated row operation to change the matrix. -Replace R2 R_{2} R2​ by 13R1+12R2 \frac{1}{3} R_{1}+\frac{1}{2} R_{2} 31​R1​+21​R2​ . [3015−2412] \left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right] [3−2​04​1512​]

Use the Gauss-Jordan method to solve the system of equations. - 8x+9y-z=48 x-4y+7z=65 2x+y+z=22

The property does not apply to matrix multiplication.

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. What is The cost of 100 batches of each candy using ingredients from supplier Y?

Solve the system of equations by using the inverse of the coefficient matrix. - x-y+z=-7 x+y+z=1 x+y-z=-1

Find the value. -Let C=[6−212];12C \mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C} C=​6−212​​;21​C

Find the inverse, if it exists, for the matrix. - A=[2−3026−6046−120600−20]A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]A=​2660​−3−6−120​000−2​2460​​

Perform the indicated operation, where possible. - [24]+[−49]\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right][2​4​]+[−49​]

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. 1.5x-0.4y+1.6z=2.4 4.5x-7.0y-0.4z=-4.0 3.8x+2.4y+2.0z=8.6

-

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=7 x-y+2z=7 2x+3z=14

Use the echelon method to solve the system of two equations in two unknowns. - 4x-2y=9 20x-10y=27

Find the ratios of products A, B, and C using a closed model. -

Find the production matrix for the input-output and demand matrices using the open model. - A=[0.20.10.50.4],D=[36]A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]A=[0.20.5​0.10.4​],D=[36​]

Linear Functions

Filters

Find the matrix product, if possible. - $\left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right]$

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ . $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $\frac{1}{3} R_{1}+\frac{1}{2} R_{2}$ . $\left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right]$

Find the value. -Let $\mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C}$

Find the inverse, if it exists, for the matrix. - $A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$

Perform the indicated operation, where possible. - $\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right]$

Find the production matrix for the input-output and demand matrices using the open model. - $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$