Compute the product or state that it is undefined.
-$$\left[ \begin{array} { r r r }
- 2 & - 2 & 6 \
5 & 8 & - 5
\end{array} \right] \left[ \begin{array} { r }
8 \
- 3 \
3
\end{array} \right]$$
A)
$\left[ \begin{array} { l } 8 \ 1 \end{array} \right]$

B)
$\left[ \begin{array} { l } 1 \ 8 \end{array} \right]$

C)
$\left[ \begin{array} { r r r } - 2 & - 2 & 6 \ 5 & 8 & - 5 \ 8 & - 3 & 3 \end{array} \right]$

D)

[8r 1 1]

Question

Compute the product or state that it is undefined.
-$$\left[ \begin{array} { r r r } 
- 2 & - 2 & 6 \
5 & 8 & - 5
\end{array} \right] \left[ \begin{array} { r } 
8 \
- 3 \
3
\end{array} \right]$$
A)
$\left[ \begin{array} { l } 8 \ 1 \end{array} \right]$

B)
$\left[ \begin{array} { l } 1 \ 8 \end{array} \right]$

C)
$\left[ \begin{array} { r r r } - 2 & - 2 & 6 \ 5 & 8 & - 5 \ 8 & - 3 & 3 \end{array} \right]$

D)

[8r 1 1]

Quizplus · Accepted Answer

To multiply a matrix by another matrix, the number of columns in the first matrix must equal the number of rows in the second matrix. Here, the first matrix is 2x3 (2 rows, 3 columns) and the second matrix is 3x1 (3 rows, 1 column), so the product is defined. The resulting matrix will have dimensions of the outer dimensions, which is 2x1 (2 rows, 1 column). The multiplication is performed as follows:For the first element of the resulting matrix:$$(-2 \times 8) + (-2 \times -3) + (6 \times 3) = -16 + 6 + 18 = 8$$For the second element of the resulting matrix:$$(5 \times 8) + (8 \times -3) + (-5 \times 3) = 40 - 24 - 15 = 1$$Thus, the product is $\left[ \begin{array} { l } 8 \ 1 \end{array} \right]$.

Compute the Product or State That It Is Undefined [−2−2658−5][8−33]\left[ \begin{array} { r r r } - 2 & - 2 & 6 \\5 & 8 & - 5\end{array} \right] \left[ \begin{array} { r } 8 \\- 3 \\3\end{array} \right][−25​−28​6−5​]​8−33​​

Compute the Product or State That It Is Undefined $\left[ \begin{array} { r r r } - 2 & - 2 & 6 \\5 & 8 & - 5\end{array} \right] \left[ \begin{array} { r } 8 \\- 3 \\3\end{array} \right]$