Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { l l }
1 & 0 \
0 & 2
\end{array} \right] , B = \left[ \begin{array} { r r r }
1 & 2 & - 2 \
2 & - 2 & 2
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 4 & - 4 & 4 \ 1 & 2 & - 2 \end{array} \right]$
B)
$$\left[ \begin{array} { r r r }
1 & 0 & 0 \
0 & - 4 & 4
\end{array} \right]$$

C) $A B$ is undefined.

D)
$$\left[ \begin{array} { r r r }
1 & 2 & - 2 \
4 & - 4 & 4
\end{array} \right]$$

Question

Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { l l } 
1 & 0 \
0 & 2
\end{array} \right] , B = \left[ \begin{array} { r r r } 
1 & 2 & - 2 \
2 & - 2 & 2
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 4 & - 4 & 4 \ 1 & 2 & - 2 \end{array} \right]$
B)
$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
0 & - 4 & 4
\end{array} \right]$$

C) $A B$ is undefined.

D)
$$\left[ \begin{array} { r r r } 
1 & 2 & - 2 \
4 & - 4 & 4
\end{array} \right]$$

Quizplus · Accepted Answer

To find the matrix product $AB$, we multiply each row of matrix $A$ by each column of matrix $B$ and sum the products. For $A = \left[ \begin{array} { l l } 1 & 0 \ 0 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 1 & 2 & - 2 \ 2 & - 2 & 2 \end{array} \right]$, the product $AB$ is $\left[ \begin{array} { r r r } 1 & 2 & - 2 \ 4 & - 4 & 4 \end{array} \right]$, because the first row of $A$ scales the first row of $B$ by 1 (leaving it unchanged), and the second row of $A$ scales the second row of $B$ by 2.

Find the Matrix Product AB, If It Is Defined A) [4−4412−2]\left[ \begin{array} { r r r } 4 & - 4 & 4 \\ 1 & 2 & - 2 \end{array} \right][41​−42​4−2​]

Find the Matrix Product AB, If It Is Defined A) $\left[ \begin{array} { r r r } 4 & - 4 & 4 \\ 1 & 2 & - 2 \end{array} \right]$