Question

find the product of the following two matrices.$\

$$\begin{bmatrix}3 & -2 & 0 & -2 \\\\0 & -5 & 3 & 4 \\\\-4 & 0 & 0 & 2 \\\\-2 & 0 & 3 & 0\\end{bmatrix}$$

\

$$\begin{bmatrix}0 \\\\-2 \\\\-4 \\\\-2\\end{bmatrix}$$

$$(3)(0) + (-2)(-2) + (0)(-4) + (-2)(-2)$

Explanation:

Step1: Calculate Row 1 result

$$\begin{aligned} (3)(0) + (-2)(-2) + (0)(-4) + (-2)(-2) &= 0 + 4 + 0 + 4 \\ &= 8 \end{aligned}$$

Step2: Calculate Row 2 result

$$\begin{aligned} (0)(0) + (-5)(-2) + (3)(-4) + (4)(-2) &= 0 + 10 - 12 - 8 \\ &= -10 \end{aligned}$$

Step3: Calculate Row 3 result

$$\begin{aligned} (-4)(0) + (0)(-2) + (0)(-4) + (2)(-2) &= 0 + 0 + 0 - 4 \\ &= -4 \end{aligned}$$

Step4: Calculate Row 4 result

$$\begin{aligned} (-2)(0) + (0)(-2) + (3)(-4) + (0)(-2) &= 0 + 0 - 12 + 0 \\ &= -12 \end{aligned}$$

Answer:

$$\begin{bmatrix} 8 \\ -10 \\ -4 \\ -12 \end{bmatrix}$$