## Precalculus (6th Edition) Blitzer

a) $A+B=\left[ \begin{matrix} 8 & 0 & -4 \\ 14 & 0 & 6 \\ -1 & 0 & 0 \\ \end{matrix} \right]$ b) $A-B=\left[ \begin{matrix} -4 & -20 & 0 \\ 14 & 24 & 14 \\ 9 & -4 & 4 \\ \end{matrix} \right]$ c) $\left( -4 \right)A=\left[ \begin{matrix} -8 & 40 & 8 \\ -56 & -48 & -40 \\ -16 & 8 & -8 \\ \end{matrix} \right]$ d) $3A+2B=\left[ \begin{matrix} 18 & -10 & -10 \\ 42 & 12 & 22 \\ 2 & -2 & 2 \\ \end{matrix} \right]$
(a) Perform the addition of the matrices $A$ and $B$ as below: \begin{align} & A+B=\left[ \begin{matrix} 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \\ \end{matrix} \right]+\left[ \begin{matrix} 6 & 10 & -2 \\ 0 & -12 & -4 \\ -5 & 2 & -2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 8 & 0 & -4 \\ 14 & 0 & 6 \\ -1 & 0 & 0 \\ \end{matrix} \right] \end{align} (b) Perform the addition of the matrices $A$ and $B$ as follows: \begin{align} & A-B=\left[ \begin{matrix} 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \\ \end{matrix} \right]-\left[ \begin{matrix} 6 & 10 & -2 \\ 0 & -12 & -4 \\ -5 & 2 & -2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -4 & -20 & 0 \\ 14 & 24 & 14 \\ 9 & -4 & 4 \\ \end{matrix} \right] \end{align} (c) Perform the addition of the matrices $A$ and $B$ as below: \begin{align} & \left( -4 \right)A=\left( -4 \right)\left[ \begin{matrix} 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -8 & 40 & 8 \\ -56 & -48 & -40 \\ -16 & 8 & -8 \\ \end{matrix} \right] \end{align} (d) Perform the addition of the matrices $A$ and $B$ as below: \begin{align} & 3A+2B=3\left[ \begin{matrix} 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \\ \end{matrix} \right]+2\left[ \begin{matrix} 6 & 10 & -2 \\ 0 & -12 & -4 \\ -5 & 2 & -2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 6 & -30 & -6 \\ 42 & 36 & 30 \\ 12 & -6 & 6 \\ \end{matrix} \right]+\left[ \begin{matrix} 12 & 20 & -4 \\ 0 & -24 & -8 \\ -10 & 4 & -4 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 18 & -10 & -10 \\ 42 & 12 & 22 \\ 2 & -2 & 2 \\ \end{matrix} \right] \end{align}