Question

Find A + B, where

a)

$\begin{array}{r}\mathbf{A}\mathbf{=}\left[\begin{array}{ccc}1& 0& 4\\ -1& 2& 2\\ 0& -2& -3\end{array}\right]\\ \mathbf{B}\mathbf{=}\left[\begin{array}{ccc}-1& 3& 5\\ 2& 2& -3\\ 2& -3& -0\end{array}\right]\end{array}$

b)

$\begin{array}{r}\mathbf{A}\mathbf{=}\left[\begin{array}{cccc}-1& 0& 5& 6\\ -4& -3& 5& -2\end{array}\right]\\ \mathbf{B}\mathbf{=}\left[\begin{array}{cccc}-3& 9& -3& 4\\ 0& -2& -1& 2\end{array}\right]\end{array}$

Short answer

a) Required matrix is$\left[\begin{array}{ccc}0& 3& 9\\ 1& 4& 4\\ 2& -5& -3\end{array}\right]$

b) Required matrix is$\left[\begin{array}{cccc}-4& 9& 2& 10\\ 4& -5& 4& 0\end{array}\right]$

Step-by-step solution

Step1: 

We have,

$\begin{array}{r}A+B=\left[\begin{array}{ccc}1& 0& 4\\ -1& 2& 2\\ 0& -2& -3\end{array}\right]+\left[\begin{array}{ccc}-1& 3& 5\\ 2& 2& -3\\ 2& -3& -0\end{array}\right]\\ =\left[\begin{array}{ccc}1+(-1)& 0+3& 4+5\\ -1+2& 2+2& 2+2\\ 0+2& -2-3& -3+0\end{array}\right]\\ =\left[\begin{array}{ccc}0& 3& 9\\ 1& 4& 4\\ 2& -5& -3\end{array}\right]\end{array}$

b)

We have,

$\begin{array}{r}A+B=\left[\begin{array}{cccc}-1& 0& 5& 6\\ -4& -3& 5& -2\end{array}\right]+\left[\begin{array}{cccc}-3& 9& -3& 4\\ 0& -2& -1& 2\end{array}\right]\\ =\left[\begin{array}{cccc}-1-3& 0+9& 5-3& 6+4\\ -4+0& -2-3& 5-1& -2+2\end{array}\right]\\ =\left[\begin{array}{cccc}-4& 9& 2& 10\\ -4& -5& 4& 0\end{array}\right]\end{array}$