Question

find the product of the following two matrices.
$\text{row 1} \
ightarrow \

$$\begin{bmatrix} 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 2 & 0 & -4 & -3 \\\\ -3 & 3 & 0 & -5 \\end{bmatrix}$$

\

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

$
$(0)(1)+(1)(1)+(1)(1)+(0)(-1)$
$\text{row 1} \
ightarrow \

$$\begin{bmatrix} \\box \\\\ \\box \\\\ \\box \\\\ \\box \\end{bmatrix}$$

$

Explanation:

Step1: Calculate Row 1 result

$(0)(1)+(1)(1)+(1)(1)+(0)(-1) = 0+1+1+0 = 2$

Step2: Calculate Row 2 result

$(0)(1)+(0)(1)+(0)(1)+(1)(-1) = 0+0+0-1 = -1$

Step3: Calculate Row 3 result

$(2)(1)+(0)(1)+(-4)(1)+(-3)(-1) = 2+0-4+3 = 1$

Step4: Calculate Row 4 result

$(-3)(1)+(3)(1)+(0)(1)+(-5)(-1) = -3+3+0+5 = 5$

Answer:

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