Answer
$a.\qquad[38 \ \ 11 \ \ 52]$
$ b.\qquad$ not defined
Work Step by Step
If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix
(so the number of columns of $A$ is the same as the number of rows of $B$),
then the matrix product $AB$ is the $m\times k$ matrix
whose $ij$-entry is the inner product of the $i\mathrm{t}\mathrm{h}$ row of $A$ and the jth column of $B.$
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$a.$
$DB$ is defined ( a $1\times 2$ matrix multiplies a $2\times 3$ matrix)
$DB $ is a $1\times 3$ matrix.
$DC$ is defined ( a $1\times 2$ matrix multiplies a $2\times 3$ matrix)
$DC $ is a $1\times 3$ matrix.
$DB+DC $ is defined as both matrices are $1\times 3$ matrices.
$DB=[7(3)+3(1) \ \ 7(1/2)+3(-1) \ \ 7(5)+3(3)]=[24 \ \ 1/2 \ \ 43]$
$DC=[7(2)+3(0) \ \ 7(-5/2)+3(2) \ \ 7(0)+3(3)]=[14 \ \ -23/2 \ \ 9]$
$DB+DC=[38 \ \ 11 \ \ 52]$
$b.$
$BF$ is defined ( a $2\times 3$ matrix multiplies a $3\times 3$ matrix)
$BF $ is a $2\times 3$ matrix.
$FE$ is defined ( a $3\times 3$ matrix multiplies a $3\times 1$ matrix)
$FE $ is a $3\times 1$ matrix.
$BF +FE $ is not defined as the matrices have different dimensions.
