## Precalculus (6th Edition) Blitzer

a) $A+B=\left[ \begin{matrix} 9 & 10 \\ 3 & 9 \\ \end{matrix} \right]$ b) $A-B=\left[ \begin{matrix} -1 & -8 \\ 3 & -5 \\ \end{matrix} \right]$ c) $\left( -4 \right)A=\left[ \begin{matrix} -16 & -4 \\ -12 & -8 \\ \end{matrix} \right]$ d) $3A+2B=\left[ \begin{matrix} 22 & 21 \\ 9 & 20 \\ \end{matrix} \right]$
(a) Perform the addition of the matrices $A$ and $B$ as follows: \begin{align} & A+B=\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]+\left[ \begin{matrix} 5 & 9 \\ 0 & 7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 4+5 & 1+9 \\ 3+0 & 2+7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 9 & 10 \\ 3 & 9 \\ \end{matrix} \right] \end{align} Hence, $A+B=\left[ \begin{matrix} 9 & 10 \\ 3 & 9 \\ \end{matrix} \right]$ (b) Perform the subtraction of the matrices $A$ and $B$ as follows: \begin{align} & A-B=\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]-\left[ \begin{matrix} 5 & 9 \\ 0 & 7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 4-5 & 1-9 \\ 3-0 & 2-7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -1 & -8 \\ 3 & -5 \\ \end{matrix} \right] \end{align} Hence, $A-B=\left[ \begin{matrix} -1 & -8 \\ 3 & -5 \\ \end{matrix} \right]$ (c) Perform the multiplication of the matrices $A$ with constant number. \begin{align} & \left( -4 \right)A=\left( -4 \right)\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -16 & -4 \\ -12 & -8 \\ \end{matrix} \right] \end{align} Hence, $\left( -4 \right)A=\left[ \begin{matrix} -16 & -4 \\ -12 & -8 \\ \end{matrix} \right]$ (d) Perform the multiplication with a content number and addition of the matrices $A$ and $B$ as follows: \begin{align} & 3A+2B=3\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]+2\left[ \begin{matrix} 5 & 9 \\ 0 & 7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 3\times 4 & 3\times 1 \\ 3\times 3 & 3\times 2 \\ \end{matrix} \right]+\left[ \begin{matrix} 2\times 5 & 2\times 9 \\ 2\times 0 & 2\times 7 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 12 & 3 \\ 9 & 6 \\ \end{matrix} \right]+\left[ \begin{matrix} 10 & 18 \\ 0 & 14 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 22 & 21 \\ 9 & 20 \\ \end{matrix} \right] \end{align} Hence, $3A+2B=\left[ \begin{matrix} 22 & 21 \\ 9 & 20 \\ \end{matrix} \right]$