Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and
the product BA. If either is not defined, say so.
-$$A = \left[ \begin{array} { r }
1 \
- 3 \
2
\end{array} \right] ; B = \left[ \begin{array} { r }
- 1 \
3 \
2
\end{array} \right]$$
A) $\mathrm { AB }$ is not defined; $\mathrm { BA }$ is not defined
B) $\mathrm { AB }$ is $1 \times 1$; BA is $1 \times 1$.
C) $A B$ is $3 \times 3$; $B A$ is $3 \times 3$.
D) $A B$ is $1 \times 1$; $B A$ is $3 \times 3$.

Question

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and
the product BA. If either is not defined, say so.
-$$A = \left[ \begin{array} { r } 
1 \
- 3 \
2
\end{array} \right] ; B = \left[ \begin{array} { r } 
- 1 \
3 \
2
\end{array} \right]$$
A) $\mathrm { AB }$ is not defined; $\mathrm { BA }$ is not defined
B) $\mathrm { AB }$ is $1 \times 1$; BA is $1 \times 1$.
C) $A B$ is $3 \times 3$; $B A$ is $3 \times 3$.
D) $A B$ is $1 \times 1$; $B A$ is $3 \times 3$.

Quizplus · Accepted Answer

Matrix $A$ is $3 \times 1$ and matrix $B$ is $3 \times 1$. The product $AB$ is not defined because the number of columns in $A$ does not match the number of rows in $B$. Similarly, the product $BA$ is not defined for the same reason.

Either the Dimensions of Two Matrices or the Matrices Themselves A=[1−32];B=[−132]A = \left[ \begin{array} { r } 1 \\- 3 \\2\end{array} \right] ; B = \left[ \begin{array} { r } - 1 \\3 \\2\end{array} \right]A=​1−32​​;B=​−132​​

Either the Dimensions of Two Matrices or the Matrices Themselves $A = \left[ \begin{array} { r } 1 \\- 3 \\2\end{array} \right] ; B = \left[ \begin{array} { r } - 1 \\3 \\2\end{array} \right]$