Question

if $g = \

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

$ and $y = 3$, what is $yg$?
if the matrix exists, select its size before entering your answer. if the matrix does not exist, select undefined.
$yg = \

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

$
1×1 1×2 1×3 1×4
2×1 2×2 2×3 2×4
3×1 3×2 3×3 3×4
4×1 4×2 4×3 4×4
undefined

Explanation:

Step1: Multiply scalar by matrix elements

To compute \(yG\), multiply each element of \(G\) by \(y=3\):
\[
3\times

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

=

$$\begin{bmatrix} 3\times(-2) & 3\times(-2) \\ 3\times3 & 3\times(-4) \end{bmatrix}$$

\]

Step2: Calculate each element

Compute the product for each position:
\[

$$\begin{bmatrix} -6 & -6 \\ 9 & -12 \end{bmatrix}$$

\]

Step3: Identify matrix size

The resulting matrix has 2 rows and 2 columns, so its size is \(2\times2\).

Answer:

Size: \(2\times2\)
\(yG =

$$\begin{bmatrix} -6 & -6 \\ 9 & -12 \end{bmatrix}$$

\)