Answer
$\left[\begin{array}{cc}{x+3}&{1-x-2w}\\{z+5}&{2r-z-17}\end{array}\right]$
Work Step by Step
If $A$ is an $m\times\boxed{n }$ matrix and $B$ is an $\boxed{n }\times k$ matrix,
then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product
of the (ith row in A) and (j-th column in B)
$(AB)_{ij}=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$.
----
$(B+C)=\left[\begin{array}{lll}
3+x & 1 & w-1\\
z+5 & r-1 & 5
\end{array}\right]$
The matrix product of a (2$\times$3) matrix and a (3$\times$2) is defined, and is a (2$\times$2) matrix.
$(B+C)A=\left[\begin{array}{lll}{3+x}&{1}&{w-1}\\{z+5}&{r-1}&{5}\end{array}\right]\left[\begin{array}{cc}{1}&{-1}\\{0}&{2}\\{0}&{-2}\end{array}\right]$
$=\left[\begin{array}{rr}
{(3+x) \cdot 1+1 \cdot 0+(w-1) \cdot 0} & (3+x)(-1)+1\cdot 2+(w-1)(-2)\\
{(z+5)\cdot 1+(r-1)\cdot 0+5\cdot 0}&{(z+5)(-1)+(r-1)\cdot 2+5(-2)}\end{array}\right]$
$=\left[\begin{array}{cc}{x+3}&{1-x-2w}\\{z+5}&{2r-z-17}\end{array}\right]$
