Question

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

$$\begin{bmatrix}4 & 4 & -9\\\\6 & -4 & -1\\end{bmatrix}$$

\

$$\begin{bmatrix}-2\\\\-4\\\\-3\\end{bmatrix}$$

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

$$\begin{bmatrix}4 & 4 & -9\\\\6 & -4 & -1\\end{bmatrix}$$

\

$$\begin{bmatrix}-2\\\\-4\\\\-3\\end{bmatrix}$$

= \

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

\\)\
\\(\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.\
submit answers show me another\
you have attempted this problem 0 times. you have 3 attempts left before new version will be requested.\
you have unlimited attempts remaining.\
email instructor\
page generated december 14, 2025, 9:39:25 pm cst\
webwork \\(\copyright\\) 1996-2025 | theme: math4-yellow | ww_version: 2.20 | pg_version 2.20\
the webwork project

Explanation:

Step1: Check matrix dimensions

First matrix: \( 2 \times 3 \) (2 rows, 3 columns). Second matrix: \( 3 \times 1 \) (3 rows, 1 column). For matrix multiplication, number of columns in first matrix (3) must equal number of rows in second matrix (3), so multiplication is defined.

Step2: Perform row - column multiplication

First row of first matrix: \( [4, 4, -9] \), second matrix: \(

$$\begin{bmatrix}-2\\-4\\-3\end{bmatrix}$$

\)
First element: \( 4\times(-2)+4\times(-4)+(-9)\times(-3)= - 8-16 + 27=3 \)

Second row of first matrix: \( [6, -4, -1] \)
Second element: \( 6\times(-2)+(-4)\times(-4)+(-1)\times(-3)=-12 + 16+3 = 7 \)

Answer:

A. \(

$$\begin{bmatrix}4&4&-9\\6&-4&-1\end{bmatrix}$$

$$\begin{bmatrix}-2\\-4\\-3\end{bmatrix}$$

=

$$\begin{bmatrix}3\\7\end{bmatrix}$$

\)