first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting five. \[\begin{array}{l} \begin{array} { l | c | c } \text { Game } 1 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 20 & 3 \\ \text { Cowens } & 16 & 5 \\ \text { Williams } & 8 & 12 \\ \text { Miller } & 6 & 11 \\ \text { Jenkins } & 10 & 2 \end{array}\\\\ \begin{array} { l | c | c } \text { Game } 2 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 18 & 4 \\ \text { Cowens } & 14 & 3 \\ \text { Williams } & 12 & 9 \\ \text { Miller } & 4 & 10 \\ \text { Jenkins } & 10 & 3 \end{array} \end{array}\]

A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -In a certain state, it is determined that 87% of all registered Republicans vote for Republican candidates, with the remainder voting for Democratic candidates. It is also determined that 84% of all registered Democrats vote For Democratic candidates, with the remainder voting for Republican candidates. The percent of voters predicted to vote For each party in the next election is given by \[\left[ \begin{array} { l } \mathrm { R } \\ \mathrm { D } \end{array} \right] = \left[ \begin{array} { l l } 0.87 & 0.16 \\ 0.13 & 0.84 \end{array} \right] \left[ \begin{array} { l } \mathrm { x } \\ \mathrm { y } \end{array} \right]\] where x is the percent of registered Republicans and y is the percent of registered Democrats. If \[\text { If } x = 53 \% \text { and } y =\] 47%, What percent of voters are predicted to vote for Democratic candidates in the next election? Round your answer To the nearest percent. A) 54% B) 87% C) 84% D) 46% A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -In a certain state, it is determined that 87% of all registered Republicans vote for Republican candidates, with the remainder voting for Democratic candidates. It is also determined that 84% of all registered Democrats vote For Democratic candidates, with the remainder voting for Republican candidates. The percent of voters predicted to vote For each party in the next election is given by \[\left[ \begin{array} { l } \mathrm { R } \\ \mathrm { D } \end{array} \right] = \left[ \begin{array} { l l } 0.87 & 0.16 \\ 0.13 & 0.84 \end{array} \right] \left[ \begin{array} { l } \mathrm { x } \\ \mathrm { y } \end{array} \right]\] where x is the percent of registered Republicans and y is the percent of registered Democrats. If \[\text { If } x = 53 \% \text { and } y =\] 47%, What percent of voters are predicted to vote for Democratic candidates in the next election? Round your answer To the nearest percent. A) 54% B) 87% C) 84% D) 46%

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting five. \[\begin{array}{l} \begin{array} { l | c | c } \text { Game } 1 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 20 & 3 \\ \text { Cowens } & 16 & 5 \\ \text { Williams } & 8 & 12 \\ \text { Miller } & 6 & 11 \\ \text { Jenkins } & 10 & 2 \end{array}\\\\ \begin{array} { l | c | c } \text { Game } 2 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 18 & 4 \\ \text { Cowens } & 14 & 3 \\ \text { Williams } & 12 & 9 \\ \text { Miller } & 4 & 10 \\ \text { Jenkins } & 10 & 3 \end{array} \end{array}\]

A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Momma's Ice Cream Shop sells three types of ice cream (soft-serve, chunky, and nonfat) at its three locations. The table below shows the number of gallons of each type sold per day at each location. $\begin{array}{l|l|l|l} \text { Gallons Sold } & \text { Soft-serve } & \text { Chunky } & \text { Nonfat } \\ \hline \text { Location I } & 29 & 80 & 30 \\ \text { Location II } & 24 & 90 & 35 \\ \text { Location III } & 60 & 120 & 40 \end{array}$ The income per gallon for soft-serve, chunky, and nonfat ice cream is $4, $6, and $8, respectively. Create two Matrices to represent these data, and use matrix multiplication to find a matrix that gives the daily income at Each location. A) $\left[ \begin{array} { l } 452 \\ 1740 \\ 840 \end{array} \right]$ B) $\left[ \begin{array} { l } 4 \\ 6 \\ 8 \end{array} \right]$ C) $\left[ \begin{array} { l } 836 \\ 916 \\ 1280 \end{array} \right]$ D) $\left[ \begin{array} { l } 896 \\ 856 \\ 1280 \end{array} \right]$ A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Momma's Ice Cream Shop sells three types of ice cream (soft-serve, chunky, and nonfat) at its three locations. The table below shows the number of gallons of each type sold per day at each location. $\begin{array}{l|l|l|l} \text { Gallons Sold } & \text { Soft-serve } & \text { Chunky } & \text { Nonfat } \\ \hline \text { Location I } & 29 & 80 & 30 \\ \text { Location II } & 24 & 90 & 35 \\ \text { Location III } & 60 & 120 & 40 \end{array}$ The income per gallon for soft-serve, chunky, and nonfat ice cream is $4, $6, and $8, respectively. Create two Matrices to represent these data, and use matrix multiplication to find a matrix that gives the daily income at Each location. A) $\left[ \begin{array} { l } 452 \\ 1740 \\ 840 \end{array} \right]$ B) $\left[ \begin{array} { l } 4 \\ 6 \\ 8 \end{array} \right]$ C) $\left[ \begin{array} { l } 836 \\ 916 \\ 1280 \end{array} \right]$ D) $\left[ \begin{array} { l } 896 \\ 856 \\ 1280 \end{array} \right]$

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting five. \[\begin{array}{l} \begin{array} { l | c | c } \text { Game } 1 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 20 & 3 \\ \text { Cowens } & 16 & 5 \\ \text { Williams } & 8 & 12 \\ \text { Miller } & 6 & 11 \\ \text { Jenkins } & 10 & 2 \end{array}\\\\ \begin{array} { l | c | c } \text { Game } 2 & \text { Points } & \text { Rebounds } \\ \hline \text { Levy } & 18 & 4 \\ \text { Cowens } & 14 & 3 \\ \text { Williams } & 12 & 9 \\ \text { Miller } & 4 & 10 \\ \text { Jenkins } & 10 & 3 \end{array} \end{array}\]

A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Assume that the table below gives the median weekly earnings in 2001 for men and women in various age groups. \[\begin{array}{l} \text { Weekly Earnings (\$) by Age Group }\\ \begin{array} { l | l | l | l | l | l | } & 16 - 24 & 25 - 34 & 35 - 44 & 45 - 54 & 55 - 64 \\ \hline \text { Men } & 375 & 680 & 520 & 706 & 777 \\ \text { Women } & 343 & 501 & 505 & 545 & 526 \end{array} \end{array}\] Suppose that, in 2002, the median weekly earnings for men increased by 7% in all age groups and the median weekly earnings for women increased by 4% in all age groups. Wha \[2 \times 2\] 2 matrix could be multiplied by the matrix below To find the median weekly earnings in 2002 for men and women in various age groups? \[\left[ \begin{array} { l l l l l } 375 & 680 & 520 & 706 & 777 \\ 343 & 501 & 505 & 545 & 526 \end{array} \right]\] A) $\left[ \begin{array} { c c } 1.07 & 0 \\ 0 & 1.04 \end{array} \right]$ B) $\left[ \begin{array} { c c } 1.04 & 0 \\ 0 & 1.07 \end{array} \right]$ C) $\left[ \begin{array} { c c } 0 & 1.07 \\ 1.04 & 0 \end{array} \right]$ D) $\left[ \begin{array} { c c } 104 & 0 \\ 0 & 107 \end{array} \right]$ A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Assume that the table below gives the median weekly earnings in 2001 for men and women in various age groups. \[\begin{array}{l} \text { Weekly Earnings (\$) by Age Group }\\ \begin{array} { l | l | l | l | l | l | } & 16 - 24 & 25 - 34 & 35 - 44 & 45 - 54 & 55 - 64 \\ \hline \text { Men } & 375 & 680 & 520 & 706 & 777 \\ \text { Women } & 343 & 501 & 505 & 545 & 526 \end{array} \end{array}\] Suppose that, in 2002, the median weekly earnings for men increased by 7% in all age groups and the median weekly earnings for women increased by 4% in all age groups. Wha \[2 \times 2\] 2 matrix could be multiplied by the matrix below To find the median weekly earnings in 2002 for men and women in various age groups? \[\left[ \begin{array} { l l l l l } 375 & 680 & 520 & 706 & 777 \\ 343 & 501 & 505 & 545 & 526 \end{array} \right]\] A) $\left[ \begin{array} { c c } 1.07 & 0 \\ 0 & 1.04 \end{array} \right]$ B) $\left[ \begin{array} { c c } 1.04 & 0 \\ 0 & 1.07 \end{array} \right]$ C) $\left[ \begin{array} { c c } 0 & 1.07 \\ 1.04 & 0 \end{array} \right]$ D) $\left[ \begin{array} { c c } 104 & 0 \\ 0 & 107 \end{array} \right]$

Exam 7: Systems of Equations and Matrices

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r r r } 0 & 5 & 0 & - 5 \\4 & 15 & - 2 & - 10 \\8 & 10 & - 4 & - 5 \\12 & 0 & - 4 & 0\end{array} \right]$

(Multiple Choice)

(Multiple Choice)

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Question 139

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting five. Game 1 Points Rebounds Levy 20 3 Cowens 16 5 Williams 8 12 Miller 6 11 Jenkins 10 2 Game 2 Points Rebounds Levy 18 4 Cowens 14 3 Williams 12 9 Miller 4 10 Jenkins 10 3 A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Assume that the table below gives the median weekly earnings in 2001 for men and women in various age groups. $\begin{array}{l}\text { Weekly Earnings (\$) by Age Group }\\\begin{array} { l | l | l | l | l | l | } & 16 - 24 & 25 - 34 & 35 - 44 & 45 - 54 & 55 - 64 \\\hline \text { Men } & 375 & 680 & 520 & 706 & 777 \\\text { Women } & 343 & 501 & 505 & 545 & 526\end{array}\end{array}$ Suppose that, in 2002, the median weekly earnings for men increased by 7% in all age groups and the median weekly earnings for women increased by 4% in all age groups. Wha $2 \times 2$ 2 matrix could be multiplied by the matrix below To find the median weekly earnings in 2002 for men and women in various age groups? $\left[ \begin{array} { l l l l l } 375 & 680 & 520 & 706 & 777 \\343 & 501 & 505 & 545 & 526\end{array} \right]$

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Question 140

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r r r } 0 & 5 & 0 & - 5 \\4 & 15 & - 2 & - 10 \\8 & 10 & - 4 & - 5 \\12 & 0 & - 4 & 0\end{array} \right]$

Find the indicated sum or difference, if it is defined. - $\left[ \begin{array} { r r } - 1 & 5 \\0 & 4 \\8 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]$

$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array} \right.$

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $2 A + B$ .

Solve using Cramer's rule, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions. - $\left\{ \begin{array} { l } 4 x + 3 y = 3 \\2 x + y = - 1\end{array} \right.$

$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x - y = 1\end{array} \right.$

Find the value of the determinant. - $\left| \begin{array} { c c } - 1 & 1 \\ 2 & 3 \end{array} \right|$

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and the product BA. If either is not defined, say so. - $A$ is $4 \times 4$ ; B is $4 \times 4$ .

$\left\{ \begin{array} { l } x - y + z = 8 \\x + y + z = 6 \\x + y - z = - 12\end{array} \right.$

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 3 \\ 0 & 2 \end{array} \right]$ . Find $3 \mathrm {~A}$ .

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r } - 1 & 3 \\0 & - 2\end{array} \right]$

The following system does not have a unique solution. Solve the system. - $\left\{ \begin{array} { c } x - y + z = 8 \\x + y + z = 6 \\3 x + y + 3 z = 10\end{array} \right.$

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and the product BA. If either is not defined, say so. - $A = \left[ \begin{array} { r } 1 \\- 3 \\2\end{array} \right] ; B = \left[ \begin{array} { r } - 1 \\3 \\2\end{array} \right]$

Use an inverse matrix to find the solution to the system. - $\left\{ \begin{aligned}x _ { 1 } + x _ { 3 } + x _ { 4 } & = 4 \\x _ { 2 } + x _ { 3 } - x _ { 4 } & = 12 \\2 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } - 3 x _ { 4 } & = 23 \\4 x _ { 2 } + 2 x _ { 4 } & = 6\end{aligned} \right.$

Write the augmented matrix associated with the system. - $\left\{ \begin{array} { c } - 2 x + 2 y + 7 z = 57 \\ 8 x - 2 y - 2 z = - 34 \\ - 2 x + 7 y + 9 z = 81 \end{array} \right.$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

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Exam 7: Systems of Equations and Matrices

Find the inverse matrix of A. - A=[050−5415−2−10810−4−5120−40]A = \left[ \begin{array} { r r r r } 0 & 5 & 0 & - 5 \\4 & 15 & - 2 & - 10 \\8 & 10 & - 4 & - 5 \\12 & 0 & - 4 & 0\end{array} \right]A=​04812​515100​0−2−4−4​−5−10−50​​

Find the indicated sum or difference, if it is defined. - [−15048−4]−[217442]\left[ \begin{array} { r r } - 1 & 5 \\0 & 4 \\8 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]​−108​54−4​​−​274​142​​

{x2+y2=25x+y=7\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array} \right.{x2+y2=25x+y=7​

Find the indicated matrix. -Let A=[3325]A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]A=[32​35​] and B=[04−16]B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]B=[0−1​46​] . Find 2A+B2 A + B2A+B .

Solve using Cramer's rule, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions. - {4x+3y=32x+y=−1\left\{ \begin{array} { l } 4 x + 3 y = 3 \\2 x + y = - 1\end{array} \right.{4x+3y=32x+y=−1​

{x2+y2=13x−y=1\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x - y = 1\end{array} \right.{x2+y2=13x−y=1​

Find the value of the determinant. - ∣−1123∣\left| \begin{array} { c c } - 1 & 1 \\ 2 & 3 \end{array} \right|​−12​13​​

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and the product BA. If either is not defined, say so. - AAA is 4×44 \times 44×4 ; B is 4×44 \times 44×4 .

{x−y+z=8x+y+z=6x+y−z=−12\left\{ \begin{array} { l } x - y + z = 8 \\x + y + z = 6 \\x + y - z = - 12\end{array} \right.⎩⎨⎧​x−y+z=8x+y+z=6x+y−z=−12​

Find the indicated matrix. -Let A=[−3302]\mathrm { A } = \left[ \begin{array} { r r } - 3 & 3 \\ 0 & 2 \end{array} \right]A=[−30​32​] . Find 3 A3 \mathrm {~A}3 A .

Find the inverse matrix of A. - A=[−130−2]A = \left[ \begin{array} { r r } - 1 & 3 \\0 & - 2\end{array} \right]A=[−10​3−2​]

The following system does not have a unique solution. Solve the system. - {x−y+z=8x+y+z=63x+y+3z=10\left\{ \begin{array} { c } x - y + z = 8 \\x + y + z = 6 \\3 x + y + 3 z = 10\end{array} \right.⎩⎨⎧​x−y+z=8x+y+z=63x+y+3z=10​

Write the augmented matrix associated with the system. - {−2x+2y+7z=578x−2y−2z=−34−2x+7y+9z=81\left\{ \begin{array} { c } - 2 x + 2 y + 7 z = 57 \\ 8 x - 2 y - 2 z = - 34 \\ - 2 x + 7 y + 9 z = 81 \end{array} \right.⎩⎨⎧​−2x+2y+7z=578x−2y−2z=−34−2x+7y+9z=81​

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Special Topics in Algebra

Filters

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r r r } 0 & 5 & 0 & - 5 \\4 & 15 & - 2 & - 10 \\8 & 10 & - 4 & - 5 \\12 & 0 & - 4 & 0\end{array} \right]$

Find the indicated sum or difference, if it is defined. - $\left[ \begin{array} { r r } - 1 & 5 \\0 & 4 \\8 & - 4\end{array} \right] - \left[ \begin{array} { l l } 2 & 1 \\7 & 4 \\4 & 2\end{array} \right]$

$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array} \right.$

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $2 A + B$ .

Solve using Cramer's rule, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions. - $\left\{ \begin{array} { l } 4 x + 3 y = 3 \\2 x + y = - 1\end{array} \right.$

$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 13 \\x - y = 1\end{array} \right.$

Find the value of the determinant. - $\left| \begin{array} { c c } - 1 & 1 \\ 2 & 3 \end{array} \right|$

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and the product BA. If either is not defined, say so. - $A$ is $4 \times 4$ ; B is $4 \times 4$ .

$\left\{ \begin{array} { l } x - y + z = 8 \\x + y + z = 6 \\x + y - z = - 12\end{array} \right.$

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 3 \\ 0 & 2 \end{array} \right]$ . Find $3 \mathrm {~A}$ .

Find the inverse matrix of A. - $A = \left[ \begin{array} { r r } - 1 & 3 \\0 & - 2\end{array} \right]$

The following system does not have a unique solution. Solve the system. - $\left\{ \begin{array} { c } x - y + z = 8 \\x + y + z = 6 \\3 x + y + 3 z = 10\end{array} \right.$

Write the augmented matrix associated with the system. - $\left\{ \begin{array} { c } - 2 x + 2 y + 7 z = 57 \\ 8 x - 2 y - 2 z = - 34 \\ - 2 x + 7 y + 9 z = 81 \end{array} \right.$