Question

problem 8. (12 points)
find the product. if it is not possible to perform this operation, explain.
\\(\

$$\begin{bmatrix}5 & -3 & -9 & 6 \\\\ 7 & -3 & 6 & -1\\end{bmatrix}$$

\

$$\begin{bmatrix}-4 & 6 \\\\ 0 & 9\\end{bmatrix}$$

\\)
select the correct choice below, and, if neccessary, fill in the answer boxes to complete your choice.
\\(\bigcirc\\) a. \\(\

$$\begin{bmatrix}5 & -3 & -9 & 6 \\\\ 7 & -3 & 6 & -1\\end{bmatrix}$$

\

$$\begin{bmatrix}-4 & 6 \\\\ 0 & 9\\end{bmatrix}$$

=\

$$\begin{bmatrix}\\square & \\square \\\\ \\square & \\square\\end{bmatrix}$$

\\)
\\(\bigcirc\\) b. the product of two matrices of different sizes is not defined.
\\(\bigcirc\\) c. the operation is not defined because the number of columns in the first matrix is not the same as the number of rows in the second matrix.
\\(\bigcirc\\) d. the operation is not defined because the number of rows in the first matrix is not the same as the number of columns in the second matrix.
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Explanation:

Step1: Check matrix dimensions

First matrix: \( 2 \) rows, \( 4 \) columns (size \( 2 \times 4 \)).
Second matrix: \( 2 \) rows, \( 2 \) columns (size \( 2 \times 2 \)).

Step2: Recall matrix multiplication rule

For matrix multiplication \( A \times B \), the number of columns in \( A \) must equal the number of rows in \( B \). Here, first matrix has \( 4 \) columns, second has \( 2 \) rows. \( 4
eq 2 \), so operation is undefined (matches option C).

Answer:

C. The operation is not defined because the number of columns in the first matrix is not the same as the number of rows in the second matrix.