Problem

9. Perform the indicated operation:
\[
\left[\begin{array}{cc}
4 & 8 \\
-10 & -3
\end{array}\right] \cdot\left[\begin{array}{cc}
-10 & 2 \\
-2 & -3
\end{array}\right]
\]
$\left[\begin{array}{cc}-53 & -18 \\ 100 & -6\end{array}\right]$
$\left[\begin{array}{cc}-51 & -22 \\ 104 & -8\end{array}\right]$
$\left[\begin{array}{cc}-56 & -16 \\ 106 & -11\end{array}\right]$
$\left[\begin{array}{cc}-62 & -18 \\ 109 & -6\end{array}\right]$
This operation cannot be performed with these matrices.

Answer

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Answer

Final Answer: The result of the matrix multiplication is \(\boxed{\left[\begin{array}{cc} -56 & -16 \\ 106 & -11 \end{array}\right]}\).

Steps

Step 1 :Given two matrices A and B, where A = \(\left[\begin{array}{cc} 4 & 8 \\ -10 & -3 \end{array}\right]\) and B = \(\left[\begin{array}{cc} -10 & 2 \\ -2 & -3 \end{array}\right]\).

Step 2 :The operation indicated is matrix multiplication. In matrix multiplication, the element in the i-th row and j-th column of the resulting matrix is the sum of the product of the elements in the i-th row of the first matrix and the j-th column of the second matrix.

Step 3 :For example, to find the element in the first row and first column of the resulting matrix, we would multiply the first element in the first row of A by the first element in the first column of B, and add that to the product of the second element in the first row of A and the second element in the first column of B.

Step 4 :Applying this process to each element in the resulting matrix to perform the matrix multiplication, we get the resulting matrix as \(\left[\begin{array}{cc} -56 & -16 \\ 106 & -11 \end{array}\right]\).

Step 5 :Final Answer: The result of the matrix multiplication is \(\boxed{\left[\begin{array}{cc} -56 & -16 \\ 106 & -11 \end{array}\right]}\).

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