The chart shows the number of personal bankruptcy filings in three City regions during various months of 2001 - 2002. \[\begin{array} { | l | l | l | l | } \hline & \text { Jan 01 } & \text { Jul 01 } & \text { Jan 02 } \\ \hline \text { North } & 140 & 140 & 140 \\ \hline \text { West } & 290 & 290 & 230 \\ \hline \text { East } & 230 & 230 & 190 \\ \hline \end{array}\] Write a matrix product whose computation gives the total number by which bankruptcy filings in January, 2001, exceeded filings in January, 2002.

A) $\left[ \begin{array} { l l l } 0 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 1 \\ - 1 \end{array} \right] = [ 110 ]$ B) $\left[ \begin{array} { l l l } 1 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } - 1 \\ 0 \\ - 1 \end{array} \right] = [ 90 ]$ C) $\left[ \begin{array} { l l l } 1 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 0 \\ - 1 \end{array} \right] = \left[ \begin{array} { c } 100 \end{array} \right]$ D) $\left[ \begin{array} { l l l } 1 & 0 & - 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { l } 1 \\ 0 \\ 1 \end{array} \right] = [ 80 ]$ E) $\left[ \begin{array} { l l l } 1 & - 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 0 \\ - 1 \end{array} \right] = [ 130 ]$ A) $\left[ \begin{array} { l l l } 0 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 1 \\ - 1 \end{array} \right] = [ 110 ]$ B) $\left[ \begin{array} { l l l } 1 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } - 1 \\ 0 \\ - 1 \end{array} \right] = [ 90 ]$ C) $\left[ \begin{array} { l l l } 1 & 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 0 \\ - 1 \end{array} \right] = \left[ \begin{array} { c } 100 \end{array} \right]$ D) $\left[ \begin{array} { l l l } 1 & 0 & - 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { l } 1 \\ 0 \\ 1 \end{array} \right] = [ 80 ]$ E) $\left[ \begin{array} { l l l } 1 & - 1 & 1 \end{array} \right] \cdot \left[ \begin{array} { l l l } 140 & 140 & 140 \\ 290 & 290 & 230 \\ 230 & 230 & 190 \end{array} \right] \cdot \left[ \begin{array} { c } 1 \\ 0 \\ - 1 \end{array} \right] = [ 130 ]$

Reduce the payoff matrix by dominance. \[\begin{array} { l } \quad\quad\quad\quad\quad\text { B } \\ \begin{array} { l l l } \quad\quad\quad\quad p & q & r \end{array} \\ A \begin{array} { l } a \\ b \end{array} \left[ \begin{array} { c c c } 2 & 0 & 10 \\ 13 & - 2 & - 7 \end{array} \right] \\ \end{array}\]

A) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad q \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 2 & 13 \\ 0 & - 2 \end{array} \right] \\ \end{array}$ B) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad q \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 2 & 0 \\ 13&-2 \end{array} \right] \\ \end{array}$ C) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&10 \\ -2&-7 \end{array} \right] \\ \end{array}$ D) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&-2\\ 10&-7 \end{array} \right] \\ \end{array}$ E) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&-2 \\ 10&-7 \end{array} \right] \\ \end{array}$ A) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad q \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 2 & 13 \\ 0 & - 2 \end{array} \right] \\ \end{array}$ B) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad q \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 2 & 0 \\ 13&-2 \end{array} \right] \\ \end{array}$ C) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&10 \\ -2&-7 \end{array} \right] \\ \end{array}$ D) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&-2\\ 10&-7 \end{array} \right] \\ \end{array}$ E) $\begin{array} { l } \quad\quad\quad\quad\text { B } \\ \quad\quad\quad\quad p \quad r \\ \mathrm { A } \begin{array} { l } a \\ { b } \end{array} \left[ \begin{array} { l l } 0&-2 \\ 10&-7 \end{array} \right] \\ \end{array}$

The following table shows sales of recreational boats in the United States during the period 1999-2001. \[\begin{array} { | l | l | l | } \hline & \text { Motorboards } & \text { Jet Skis } \\ \hline 1999 & 310,000 & 110,000 \\ \hline \text { Increase in } 2000 & 9,000 & 0 \\ \hline \text { Increase in } 2001 & - 40,000 & - 40,000 \\ \hline \end{array}\] Write the matrix algebra formula that will find the sales in each category.

A) $\left[ \begin{array} { l } 310,000 \\ 110,000 \end{array} \right] + \left[ \begin{array} { c } 9,000 \\ - 40,000 \end{array} \right] + \left[ \begin{array} { c } 0 \\ - 40,000 \end{array} \right]$ B) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & 0 \end{array} \right] - \left[ \begin{array} { l l l } - 40,000 & - 40,000 \end{array} \right]$ C) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & 0 \end{array} \right] + \left[ \begin{array} { l l l } - 40,000 & - 40,000 \end{array} \right]$ D) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & - 40,000 \end{array} \right] + \left[ \begin{array} { l l } 0 & - 40,000 \end{array} \right]$ E) $\left[ \begin{array} { l } 310,000 \\ 110,000 \end{array} \right] + \left[ \begin{array} { c } 9,000 \\ 0 \end{array} \right] + \left[ \begin{array} { l } 40,000 \\ 40,000 \end{array} \right]$ A) $\left[ \begin{array} { l } 310,000 \\ 110,000 \end{array} \right] + \left[ \begin{array} { c } 9,000 \\ - 40,000 \end{array} \right] + \left[ \begin{array} { c } 0 \\ - 40,000 \end{array} \right]$ B) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & 0 \end{array} \right] - \left[ \begin{array} { l l l } - 40,000 & - 40,000 \end{array} \right]$ C) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & 0 \end{array} \right] + \left[ \begin{array} { l l l } - 40,000 & - 40,000 \end{array} \right]$ D) $\left[ \begin{array} { l l l } 310,000 & 110,000 \end{array} \right] + \left[ \begin{array} { l l } 9,000 & - 40,000 \end{array} \right] + \left[ \begin{array} { l l } 0 & - 40,000 \end{array} \right]$ E) $\left[ \begin{array} { l } 310,000 \\ 110,000 \end{array} \right] + \left[ \begin{array} { c } 9,000 \\ 0 \end{array} \right] + \left[ \begin{array} { l } 40,000 \\ 40,000 \end{array} \right]$

Two sectors of any country economy are (1) lumber and wood products and (2) paper and allied products. In 1998 the input-output table involving these two sectors was as follows (all figures are in millions of dollars). \[\begin{array} { | r | c | c | } \hline \text { To } & \text { Wood } & \text { Paper } \\ \hline \text { From Wood } & 36,000 & 7,000 \\ \hline \text { Paper } & 100 & 17,000 \\ \hline \text { Total Output } & 120,000 & 120,000 \\ \hline \end{array}\] If external demand for lumber and wood products rises by $14,000 million and external demand for paper and allied products rises by $22,000 million, what increase in output of these two sectors is necessary Round answers to two significant digits.

A) increase in output of lumber and wood products is $22,137.71 million and increase in output of paper and allied products is $25,652.56 million B) increase in output of lumber and wood products is $24,137.71 million and increase in output of paper and allied products is $28,652.56 million C) increase in output of lumber and wood products is $21,137.71 million and increase in output of paper and allied products is $25,652.56 million D) increase in output of lumber and wood products is $19,137.71 million and increase in output of paper and allied products is $23,652.56 million E) increase in output of lumber and wood products is $22,137.71 million and increase in output of paper and allied products is $23,652.56 million A) increase in output of lumber and wood products is $22,137.71 million and increase in output of paper and allied products is $25,652.56 million B) increase in output of lumber and wood products is $24,137.71 million and increase in output of paper and allied products is $28,652.56 million C) increase in output of lumber and wood products is $21,137.71 million and increase in output of paper and allied products is $25,652.56 million D) increase in output of lumber and wood products is $19,137.71 million and increase in output of paper and allied products is $23,652.56 million E) increase in output of lumber and wood products is $22,137.71 million and increase in output of paper and allied products is $23,652.56 million

Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars) \[\begin{array} { | r | r | r | r | r | } \hline \text { To } & 1& 2 & 3 & 4 \\ \hline \text { From 1 } & 11,109 & 10 & 100 & 995 \\ \hline \mathbf { 2 } & 25,329 & 4,303 & 0 & 4,957 \\ \hline \mathbf { 3 } & 0 & 0 & 441 & 57 \\ \hline \mathbf { 4 } & 5,425 & 11,060 & 3,437 & 153 \\ \hline \text { Total Output } & 101,418 & 121,752 & 14,428 & 46,814 \\ \hline \end{array}\] Determine how these four sectors would react to an increase in demand for Sector 1 production of $1,000 million. Round your answers to two decimal places. Express the answer as a column matrix.

The answer of Four sectors of some economy are (1)...

Exam 5: Matrix Algebra and Applications

Let $A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]$ and $B = \left[ \begin{array} { c c } 7 & - 2 \\4 & 12 \\9 & - 2\end{array} \right]$ , evaluate $- 2 A + B$ .

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Question 173

Decide whether the game is strictly determined. B A a b c -2 -5 9 1 1 0 -1 -2 -3 1 1 -1 (answer strictly determined or not strictly determined) If it is, what are the players' optimal pure strategies A B What is the value of the game

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Question 174

Let $A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]$ and $B = \left[ \begin{array} { c c } 7 & - 2 \\4 & 12 \\9 & - 2\end{array} \right]$ , evaluate $- 2 A + B$ .

Translate the given system of equations into matrix form. $\left\{ \begin{array} { r } x + y - z = 8 \\3 x + y + z = 5 \\\frac { 3 x } { 2 } + \frac { z } { 4 } = 9\end{array} \right\}$

Find the dimensions of the matrix $B = \left[ \begin{array} { c } \frac { 2 } { 3 } \\3 \\0 \\- \frac { 4 } { 7 }\end{array} \right]$ And identify the value of the element $b _ { 21 }$ .

Reduce the payoff matrix by dominance. B p q r A a b 2 0 10 13 -2 -7

The following table shows sales of recreational boats in the United States during the period 1999-2001. Motorboards Jet Skis 1999 310,000 110,000 Increase in 2000 9,000 0 Increase in 2001 -40,000 -40,000 Write the matrix algebra formula that will find the sales in each category.

Perform the indicated operations. $\frac { 1 } { 2 } \left[ \begin{array} { c c c } 28 & 14 & 10 \\4 & 0 & 2\end{array} \right] - 3 \left[ \begin{array} { c c c } 1 & 0 & 1 \\- 1 & 1 & - 1\end{array} \right]$

Find the dimensions of the matrix $A = \left[ \begin{array} { l l l l } - 1 & 2 & 0 & 3\end{array} \right]$ And identify the value of the element $Q _ { 14 }$ .

Solve for x, y, and z. $\left[ \begin{array} { c c c } 6 y & x - 2 & 3 z \\x & z & 9 z\end{array} \right] = \left[ \begin{array} { c c c } 18 z & y & - 9 \\y + 2 & - 3 & 3 y\end{array} \right]$ $x =$ $y =$ $z =$ __

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c } 1 & 5 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

Decide whether the game is strictly determined. B A a b c -2 -5 9 1 1 0 -1 -2 -3 1 1 -1 (answer strictly determined or not strictly determined) If it is, what are the players' optimal pure strategies A B What is the value of the game

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Exam 5: Matrix Algebra and Applications

Let A=[10−2265]A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]A=​1−26​025​​ and B=[7−24129−2]B = \left[ \begin{array} { c c } 7 & - 2 \\4 & 12 \\9 & - 2\end{array} \right]B=​749​−212−2​​ , evaluate −2A+B- 2 A + B−2A+B .

Translate the given system of equations into matrix form. ​ {x+y−z=83x+y+z=53x2+z4=9}\left\{ \begin{array} { r } x + y - z = 8 \\3 x + y + z = 5 \\\frac { 3 x } { 2 } + \frac { z } { 4 } = 9\end{array} \right\}⎩⎨⎧​x+y−z=83x+y+z=523x​+4z​=9​⎭⎬⎫​

Find the dimensions of the matrix B=[2330−47]B = \left[ \begin{array} { c } \frac { 2 } { 3 } \\3 \\0 \\- \frac { 4 } { 7 }\end{array} \right]B=​32​30−74​​​ And identify the value of the element b21b _ { 21 }b21​ .

Reduce the payoff matrix by dominance. B p q r A a b 2 0 10 13 -2 -7

The following table shows sales of recreational boats in the United States during the period 1999-2001. Motorboards Jet Skis 1999 310,000 110,000 Increase in 2000 9,000 0 Increase in 2001 -40,000 -40,000 Write the matrix algebra formula that will find the sales in each category.

Perform the indicated operations. 12[281410402]−3[101−11−1]\frac { 1 } { 2 } \left[ \begin{array} { c c c } 28 & 14 & 10 \\4 & 0 & 2\end{array} \right] - 3 \left[ \begin{array} { c c c } 1 & 0 & 1 \\- 1 & 1 & - 1\end{array} \right]21​[284​140​102​]−3[1−1​01​1−1​]

Find the dimensions of the matrix A=[−1203]A = \left[ \begin{array} { l l l l } - 1 & 2 & 0 & 3\end{array} \right]A=[−1​2​0​3​] And identify the value of the element Q14Q _ { 14 }Q14​ .

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. ​ [15−145−4−145]\left[ \begin{array} { c c c } 1 & 5 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]​14−1​554​−1−45​​

Decide whether the game is strictly determined. B A a b c -2 -5 9 1 1 0 -1 -2 -3 1 1 -1 __________ (answer strictly determined or not strictly determined) If it is, what are the players' optimal pure strategies A __________ B __________ What is the value of the game __________

Functions and Applications

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Let $A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]$ and $B = \left[ \begin{array} { c c } 7 & - 2 \\4 & 12 \\9 & - 2\end{array} \right]$ , evaluate $- 2 A + B$ .

Translate the given system of equations into matrix form. $\left\{ \begin{array} { r } x + y - z = 8 \\3 x + y + z = 5 \\\frac { 3 x } { 2 } + \frac { z } { 4 } = 9\end{array} \right\}$

Find the dimensions of the matrix $B = \left[ \begin{array} { c } \frac { 2 } { 3 } \\3 \\0 \\- \frac { 4 } { 7 }\end{array} \right]$ And identify the value of the element $b _ { 21 }$ .

Perform the indicated operations. $\frac { 1 } { 2 } \left[ \begin{array} { c c c } 28 & 14 & 10 \\4 & 0 & 2\end{array} \right] - 3 \left[ \begin{array} { c c c } 1 & 0 & 1 \\- 1 & 1 & - 1\end{array} \right]$

Find the dimensions of the matrix $A = \left[ \begin{array} { l l l l } - 1 & 2 & 0 & 3\end{array} \right]$ And identify the value of the element $Q _ { 14 }$ .

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c } 1 & 5 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

Decide whether the game is strictly determined. B A a b c -2 -5 9 1 1 0 -1 -2 -3 1 1 -1 (answer strictly determined or not strictly determined) If it is, what are the players' optimal pure strategies A B What is the value of the game