Question

consider these three matrices.
$a = \

$$\begin{bmatrix}5\\\\7\\\\9\\end{bmatrix}$$

$, $b = \

$$\begin{bmatrix}-1\\\\2\\\\3\\end{bmatrix}$$

$, $c = \

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

$
what is the result of evaluating the matrix expression $b - 2a + c$
enter the correct answer in the box. use the matrix button to enter your answer i

Explanation:

Step1: Calculate scalar multiple $2A$

Multiply each element of $A$ by 2:

$$2A = 2
LATEXBLOCK1
=
LATEXBLOCK2
=
LATEXBLOCK3
$$

Step2: Substitute into the expression

Replace $2A$ in $B - 2A + C$:

$$B - 2A + C =
LATEXBLOCK4
-
LATEXBLOCK5
+
LATEXBLOCK6
$$

Step3: Perform element-wise operations

Subtract and add corresponding elements:

$$\begin{bmatrix}-1-10+2\\2-14+2\\3-18+4\end{bmatrix} = \begin{bmatrix}-9\\-10\\-11\end{bmatrix}$$

Answer:

$$\begin{bmatrix}-9\\-10\\-11\end{bmatrix}$$