Question

if $c = \

$$\begin{bmatrix}-6 & -1 & -3\\\\ -2 & 4 & -1\\end{bmatrix}$$

$ and $t = -8$, what is $tc$? if the matrix exists, select its size before entering your answer. if the matrix does not exist, select undefined. $tc = \

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

$

Explanation:

Step1: Identify matrix size of C

Matrix $C$ is a $2 \times 3$ matrix.

Step2: Multiply scalar t by each element

Multiply every element in $C$ by $t=-8$:
First row: $-8 \times (-6) = 48$, $-8 \times (-1) = 8$, $-8 \times (-3) = 24$
Second row: $-8 \times (-2) = 16$, $-8 \times 4 = -32$, $-8 \times (-1) = 8$

Step3: Confirm resulting matrix size

Scalar multiplication preserves the matrix size, so $tC$ is $2 \times 3$.

Answer:

Size: $2 \times 3$
$tC =

$$\begin{bmatrix} 48 & 8 & 24 \\ 16 & -32 & 8 \end{bmatrix}$$

$