Question

find the product of the following two matrices.
row 1 $
ightarrow \begin{bmatrix} 2 & 5 & 0 \\ 0 & 1 & -1 end{bmatrix} \begin{bmatrix} -1 & 1 \\ 0 & 1 \\ -1 & 0 end{bmatrix}$
$(2)(-1)+(5)(0)+(0)(-1)$
row 1 $
ightarrow \begin{bmatrix} square & square \\ square & square end{bmatrix}$

Explanation:

Step1: Calculate (1,1) entry

$$\begin{align*} (2)(-1)+(5)(0)+(0)(-1) &= -2 + 0 + 0 \\ &= -2 \end{align*}$$

Step2: Calculate (1,2) entry

$$\begin{align*} (2)(1)+(5)(1)+(0)(0) &= 2 + 5 + 0 \\ &= 7 \end{align*}$$

Step3: Calculate (2,1) entry

$$\begin{align*} (0)(-1)+(1)(0)+(-1)(-1) &= 0 + 0 + 1 \\ &= 1 \end{align*}$$

Step4: Calculate (2,2) entry

$$\begin{align*} (0)(1)+(1)(1)+(-1)(0) &= 0 + 1 + 0 \\ &= 1 \end{align*}$$

Answer:

$$\begin{bmatrix} -2 & 7 \\ 1 & 1 \end{bmatrix}$$