Answer
$a.\quad DH=[27 \ \ 4]$
$ b.\quad$ 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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D is a 1$\times$2 matrix. H is a 2$\times$2 matrix
$a.$
$DH$ is defined, and is a 1$\times$2 matrix
$[DH]_{11}$= (row 1 in D) times (column 1 in H)$=7(3)+3(2)=27$
$[DH]_{12}$= (row 1 in D) times (column 2 in H)$=7(1)+3(-1)=4$
$DH=[27 \ \ 4]$
$b.$
$HD$ is not defined, H is a 2$\times$2 matrix, and has two columns.
D does not have 2 rows needed for multiplication.
