Exam 48: Operations With Matrices

Find A + B.​ $A = \left[ \begin{array} { c c } 9 & - 2 \\3 & 2 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c } 2 & 7 \\- 2 & - 5 \\2 & 8\end{array} \right]$ ​

Of the products AB,BA,A² and B²,which ones are possible for the given matrices? $A = \left[ \begin{array} { c } - 3 \\1 \\- 7\end{array} \right] , B = \left[ \begin{array} { l l l } 7 & 1 & 6\end{array} \right]$

If possible,find AB. $A = \left[ \begin{array} { l } - 5 \\- 1\end{array} \right] , B = \left[ \begin{array} { c c } 1 & - 2 \\- 6 & 3 \\- 6 & - 5\end{array} \right]$

Evaluate the expression. $\left[ \begin{array} { c c } 3 & - 4 \\- 1 & 5\end{array} \right] \left[ \begin{array} { l l } - 5 & 2 \\- 4 & 1\end{array} \right] \left[ \begin{array} { c c } - 1 & - 2 \\2 & 4\end{array} \right]$

If possible,find 3A + 2B. $A = \left[ \begin{array} { c c c } - 5 & 1 & 4 \\- 4 & 3 & - 1\end{array} \right] , B = \left[ \begin{array} { c c c } - 1 & - 3 & - 7 \\6 & - 2 & - 5\end{array} \right]$

Find A + B.​ $A = \left[ \begin{array} { l l l } 5 & 5 & 4 \\9 & 9 & 2\end{array} \right] , B = \left[ \begin{array} { l l l } 3 & 7 & 8 \\7 & 6 & 4\end{array} \right]$

Use the matrix capabilities of a graphing utility to find AB,if possible. $A = \left[ \begin{array} { c c } 4 & - 5 \\- 4 & 2 \\- 3 & - 9 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c c c } - 1 & - 9 & 8 & - 7 \\- 9 & - 1 & - 1 & 9\end{array} \right]$

A lawn-and-garden store sells three types of fertilizer in 50-pound bags: Feed & Weed,Winterizer Blend,and 17-17-17.The number of bags that were sold last weekend is represented by A. The selling price per bag and the profit per bag for the three types of fertilizer are represented by B (values are in dollars).​ $Selling~ Price~~~ Profit$ Bequals open bracket 11.50 1.20 13.25 1.50 8.25 0.70 close bracket Feed \& Weed Winterizer 17-17-17 Compute AB and interpret the result.

Find A - B.​ $A = \left[ \begin{array} { c c c } - 2 & 5 & 0 \\3 & - 4 & 4 \\6 & 6 & - 1 \\0 & 8 & - 2 \\- 4 & - 4 & 0\end{array} \right] , B = \left[ \begin{array} { c c c } - 4 & 8 & 2 \\4 & - 4 & - 4 \\11 & - 8 & - 4 \\2 & 2 & - 4 \\0 & 1 & - 1\end{array} \right]$ ​

Use the matrix capabilities of a graphing utility to evaluate the expression.Round your results to three decimal places,if necessary.​ $55 \left( \left[ \begin{array} { c c } 12 & - 18 \\- 17 & 19\end{array} \right] + \left[ \begin{array} { c c } - 21 & 13 \\15 & 14\end{array} \right] \right)$ ​

If possible,find AB and state the order of the result.​ $A = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & - 3\end{array} \right] , B = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & - 5 & 0 \\0 & 0 & 4\end{array} \right]$ ​

Of the products AB,BA,A² and B²,which ones are possible for the given matrices? $A = \left[ \begin{array} { l l } 1 & 1 \\6 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 5 & - 6 \\- 7 & 3\end{array} \right]$

Find the product.​ $\left[ \begin{array} { l l } 9 & 3 \\7 & 8\end{array} \right] \left[ \begin{array} { l l } 8 & 7 \\8 & 4\end{array} \right]$ ​

Find 3A - 2B.​ $A = \left[ \begin{array} { c c } 6 & - 4 \\4 & 4 \\- 4 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 4 \\- 1 & - 6 \\2 & 10\end{array} \right]$ ​

Find A + B.​ $A = \left[ \begin{array} { l l } 5 & - 5 \\2 & - 5\end{array} \right] , B = \left[ \begin{array} { c c } 2 & - 5 \\- 5 & 7\end{array} \right]$ ​

Write the system of linear equations as a matrix equation,AX = B.​ $\left\{ \begin{array} { r } - x _ { 1 } + x _ { 2 } = 8 \\- 4 x _ { 1 } + x _ { 2 } = 0\end{array} \right.$ ​

Use the matrix capabilities of a graphing utility to evaluate the expression.Round your results to three decimal places,if necessary.​ $\frac { 3 } { 7 } \left[ \begin{array} { c c } - 6 & 6 \\2 & - 4\end{array} \right] + 6 \left[ \begin{array} { c c } 8 & 2 \\- 5 & - 4\end{array} \right]$ ​

A corporation has three factories,each of which manufactures acoustic guitars and electric guitars.The number of units of guitars produced at factory j in one day is represented by a_ij in the matrix​ $A = \left[ \begin{array} { c c c } 50 & 30 & 35 \\25 & 100 & 60\end{array} \right]$ . ​ Find the production levels if production is increased by 20%. ​

If possible,find AB and state the order of the result.​ $A = \left[ \begin{array} { c c c } 0 & 3 & 0 \\4 & 0 & 3 \\4 & 6 & - 3\end{array} \right] , B = \left[ \begin{array} { c c } - 1 & 8 \\2 & - 2 \\10 & - 9\end{array} \right]$ ​