Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { r r r }
1 & 3 & - 1 \
3 & 0 & 5
\end{array} \right] , B = \left[ \begin{array} { r r }
3 & 0 \
- 1 & 1 \
0 & 5
\end{array} \right]$$
A)
$\left[ \begin{array} { l l } 0 & - 2 \ 9 & 25 \end{array} \right]$

B)

$\left[ \begin{array} { c c } - 2 & 0 \ 25 & 9 \end{array} \right]$

C) $\mathrm { AB }$ is undefined.

D)
$$\left[ \begin{array} { r r r }
3 & - 3 & 0 \
0 & 0 & 25
\end{array} \right]$$

Question

Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { r r r } 
1 & 3 & - 1 \
3 & 0 & 5
\end{array} \right] , B = \left[ \begin{array} { r r } 
3 & 0 \
- 1 & 1 \
0 & 5
\end{array} \right]$$
A)
$\left[ \begin{array} { l l } 0 & - 2 \ 9 & 25 \end{array} \right]$

B)

$\left[ \begin{array} { c c } - 2 & 0 \ 25 & 9 \end{array} \right]$

C) $\mathrm { AB }$ is undefined.

D)
$$\left[ \begin{array} { r r r } 
3 & - 3 & 0 \
0 & 0 & 25
\end{array} \right]$$

Quizplus · Accepted Answer

The product of matrices A (2x3) and B (3x2) is defined and results in a 2x2 matrix. The elements of the resulting matrix are calculated by taking the dot product of rows from A with columns from B. For the first element, (1*3) + (3*-1) + (-1*0) = 3 - 3 + 0 = 0. Following this method for all elements gives the matrix $\left[ \begin{array} { l l } 0 & - 2 \ 9 & 25 \end{array} \right]$.

Find the Matrix Product AB, If It Is Defined A) [0−2925]\left[ \begin{array} { l l } 0 & - 2 \\ 9 & 25 \end{array} \right][09​−225​]

Find the Matrix Product AB, If It Is Defined A) $\left[ \begin{array} { l l } 0 & - 2 \\ 9 & 25 \end{array} \right]$