Question

move to problem: |1|2|3|4|5|6|7|8|
problem 5. (12 points)
let ( a = \begin{bmatrix}-9 & -2 \\ -2 & -5end{bmatrix} ) and ( b = \begin{bmatrix}-1 & -5 \\ -2 & -2end{bmatrix} ).
find ( -3a - 2b ).
select the correct choice below, and, if neccessary, fill in the answer boxes to complete your choice.
( \bigcirc ) a. ( -3a - 2b = \begin{bmatrix}square & square \\ square & squareend{bmatrix} )
( \bigcirc ) b. the simplification is not possible.
move to problem: |1|2|3|4|5|6|7|8|
grade test
note: grading the test grades all problems, not just those on this page.
page generated december 14, 2025, 9:54:30 pm cst
webwork © 1996-2025 | theme: math4-yellow | ww_version: 2.20 | pg_version 2.20
the webwork project

Explanation:

Step1: Calculate -3A

To find \(-3A\), we multiply each element of matrix \(A\) by \(-3\). Given \(A =

$$\begin{bmatrix}-9&-2\\-2&-5\end{bmatrix}$$

\), we have:

$$ -3A = -3
LATEXBLOCK1
=
LATEXBLOCK2
=
LATEXBLOCK3
$$

Step2: Calculate -2B

To find \(-2B\), we multiply each element of matrix \(B\) by \(-2\). Given \(B =

$$\begin{bmatrix}-1&-5\\-2&-2\end{bmatrix}$$

\), we have:

$$ -2B = -2
LATEXBLOCK5
=
LATEXBLOCK6
=
LATEXBLOCK7
$$

Step3: Add -3A and -2B

Now we add the two resulting matrices \(-3A\) and \(-2B\) together. To add matrices, we add the corresponding elements:

$$ -3A - 2B = -3A + (-2B) =
LATEXBLOCK8
=
LATEXBLOCK9
$$

Answer:

A. \(-3A - 2B =

$$\begin{bmatrix}29&16\\10&19\end{bmatrix}$$

\)