Problem

Find the following matrices where $A=\left[\begin{array}{ll}9 & 2 \\ 6 & 6\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 8 \\ 1 & 3\end{array}\right]$.
a. $A+B$
b. $A-B$
c. $-5 \mathrm{~A}$
d. $3 \mathrm{~A}+4 \mathrm{~B}$
a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $A+B=\square$ (Simplify your answer.)
B. This matrix operation is not possible.

Answer

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Answer

Final Answer: \(\boxed{\left[\begin{array}{ll}10 & 10 \\ 7 & 9\end{array}\right]}\)

Steps

Step 1 :Given matrices A and B as $A=\left[\begin{array}{ll}9 & 2 \ 6 & 6\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 8 \ 1 & 3\end{array}\right]$ respectively.

Step 2 :To find the sum of the matrices A and B, we perform matrix addition. This is done element by element. That is, the element in the i-th row and j-th column of the resulting matrix is the sum of the elements in the i-th row and j-th column of the two matrices being added.

Step 3 :Adding the corresponding elements of matrices A and B, we get $A+B=\left[\begin{array}{ll}10 & 10 \ 7 & 9\end{array}\right]$

Step 4 :Final Answer: \(\boxed{\left[\begin{array}{ll}10 & 10 \\ 7 & 9\end{array}\right]}\)

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