Question

find the product of the following two matrices. $\begin{bmatrix} -5&4&0\\ -2&0&-3\\ 0&0&-2end{bmatrix} \begin{bmatrix} -1&-1&1\\ -2&-1&0\\ 1&0&-4end{bmatrix}$

Explanation:

Step1: Calculate row1-col1 entry

$(-5)(-1) + (4)(-2) + (0)(1) = 5 - 8 + 0 = -3$

Step2: Calculate row1-col2 entry

$(-5)(-1) + (4)(-1) + (0)(0) = 5 - 4 + 0 = 1$

Step3: Calculate row1-col3 entry

$(-5)(1) + (4)(0) + (0)(-4) = -5 + 0 + 0 = -5$

Step4: Calculate row2-col1 entry

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

Step5: Calculate row2-col2 entry

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

Step6: Calculate row2-col3 entry

$(-2)(1) + (0)(0) + (-3)(-4) = -2 + 0 + 12 = 10$

Step7: Calculate row3-col1 entry

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

Step8: Calculate row3-col2 entry

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

Step9: Calculate row3-col3 entry

$(0)(1) + (0)(0) + (-2)(-4) = 0 + 0 + 8 = 8$

Answer:

$$\begin{bmatrix} -3 & 1 & -5 \\ -1 & 2 & 10 \\ -2 & 0 & 8 \end{bmatrix}$$