Find AB, if possible.
-$A = \left[ \begin{array} { c c } 2 & - 1 \ 6 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 6 & 2 \ 1 & 6 \end{array} \right]$
A) Not possible

B) $\left[ \begin{array} { c c } 12 & - 2 \ 6 & 30 \end{array} \right]$

C) $\left[ \begin{array} { l l } - 2 & 12 \ 30 & 6 \end{array} \right]$

D) $\left[ \begin{array} { l l } 11 & - 2 \ 4 & 42 \end{array} \right]$

Question

Find AB, if possible.
-$A = \left[ \begin{array} { c c } 2 & - 1 \ 6 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 6 & 2 \ 1 & 6 \end{array} \right]$
A) Not possible

B) $\left[ \begin{array} { c c } 12 & - 2 \ 6 & 30 \end{array} \right]$

C) $\left[ \begin{array} { l l } - 2 & 12 \ 30 & 6 \end{array} \right]$

D) $\left[ \begin{array} { l l } 11 & - 2 \ 4 & 42 \end{array} \right]$

Quizplus · Accepted Answer

To find the product $AB$, we multiply each row of matrix $A$ by each column of matrix $B$ and sum the products. The resulting matrix is $\left[ \begin{array} { c c } (2*6 + (-1)*1) & (2*2 + (-1)*6) \ (6*6 + 5*1) & (6*2 + 5*6) \end{array} \right] = \left[ \begin{array} { c c } 11 & -2 \ 36 + 5 & 12 + 30 \end{array} \right] = \left[ \begin{array} { l l } 11 & -2 \ 41 & 42 \end{array} \right]$. However, there seems to be a mistake in my calculation or in the provided options, as none of the options exactly match the correct calculation. The correct calculation should yield a matrix based on the described method, but it appears I made an error in the final step of my explanation. The correct calculation for the second row, first column should indeed be $6*6 + 5*1 = 36 + 5 = 41$, but the correct option should reflect the proper multiplication and addition of elements from matrices $A$ and $B$. Given the options, none exactly match the expected outcome of the multiplication based on standard matrix multiplication rules, indicating a mistake in my explanation regarding the final values. The correct approach to find $AB$ involves multiplying corresponding elements and summing them up for each position in the resulting matrix, which should be carefully checked against the provided options.

Find AB, If Possible A=[2−165]A = \left[ \begin{array} { c c } 2 & - 1 \\ 6 & 5 \end{array} \right]A=[26​−15​]

Find AB, If Possible $A = \left[ \begin{array} { c c } 2 & - 1 \\ 6 & 5 \end{array} \right]$