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the answer is not correct.
find the product. if it is not possible to perform this operation, explain.
\\(\

$$\begin{bmatrix}-3 & -4 & -7 & -9 \\\\ 2 & 6 & -8 & 5\\end{bmatrix}$$

\

$$\begin{bmatrix}-5 & -5 \\\\ 8 & -7\\end{bmatrix}$$

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

$$\begin{bmatrix}-3 & -4 & -7 & -9 \\\\ 2 & 6 & -8 & 5\\end{bmatrix}$$

\

$$\begin{bmatrix}-5 & -5 \\\\ 8 & -7\\end{bmatrix}$$

= \

$$\begin{bmatrix}-42 & -66 \\\\ 68 & 94\\end{bmatrix}$$

\\)
\\(\bigcirc\\) b. 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.
\\(\bigcirc\\) c. the product of two matrices of different sizes is not defined.
\\(\bigcirc\\) d. 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.
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Explanation:

Step1: Recall Matrix Multiplication Rule

For matrix multiplication, if matrix \( A \) has dimensions \( m \times n \) and matrix \( B \) has dimensions \( p \times q \), the product \( AB \) is defined only if \( n = p \). The resulting matrix will have dimensions \( m \times q \).

Step2: Determine Dimensions of Given Matrices

• First matrix: \(

$$\begin{bmatrix}-3&-4&-7&-9\\2&6&-8&5\end{bmatrix}$$

\) has \( 2 \) rows and \( 4 \) columns (so \( m = 2 \), \( n = 4 \)).

• Second matrix: \(

$$\begin{bmatrix}-5&-5\\8&-7\end{bmatrix}$$

\) has \( 2 \) rows and \( 2 \) columns (so \( p = 2 \), \( q = 2 \)).

Step3: Check if Multiplication is Defined

We need \( n = p \) for \( AB \) to be defined. Here, \( n = 4 \) (columns of first matrix) and \( p = 2 \) (rows of second matrix). Since \( 4
eq2 \), 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.

Answer:

D. 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.