Answer:
B
Step-by-step explanation:
When adding two matrices of the same dimensions we addup each two corresponding elements of these matrices:
[tex]A+B=\left[\begin{array}{cc}8&-3\\3&y+2\end{array}\right]+\left[\begin{array}{cc}3x&z+4\\w&\frac{1}{2}y\end{array}\right]=\left[\begin{array}{cc}8+3x&-3+z+4\\3+w&y+2+\frac{1}{2}y\end{array}\right].[/tex]
When two matrices are equal, then corresponding elements are equal:
[tex]\left\{\begin{array}{l}8+3x=x\\-3+z+4=2z\\3+w=4\\y+2+\frac{1}{2}y=y\end{array}\right.\Rightarrow \left\{\begin{array}{l}x=-4\\z=1\\w=1\\y=-4\end{array}\right.[/tex]
Hence,
[tex]B=\left[\begin{array}{cc}-12&5\\1&-2\end{array}\right].[/tex]
