Multiply matrices A and B, where A = [[2, 1, −1], [0, 3, 2]] and B = [[1, 0], [3, −1], [−1, 2]].

Question

ScanSolve AI Tutor · Accepted Answer

Alright, Hurry, let's multiply these matrices.

We are given two matrices:

A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & 2 \end{bmatrix}

B = \begin{bmatrix} 1 & 0 \\ 3 & -1 \\ -1 & 2 \end{bmatrix}

To find the product $AB$ , we multiply the rows of matrix $A$ by the columns of matrix $B$ . The resulting matrix will be a $2 \times 2$ matrix.

Calculate the element in the first row, first column ( $c_{11}$ ).
Multiply the first row of $A$ by the first column of $B$ :
$c_{11} = (2)(1) + (1)(3) + (-1)(-1)$ $c_{11} = 2 + 3 + 1 = 6$
Calculate the element in the first row, second column ( $c_{12}$ ).
Multiply the first row of $A$ by the second column of $B$ :
$c_{12} = (2)(0) + (1)(-1) + (-1)(2)$ $c_{12} = 0 - 1 - 2 = -3$
Calculate the element in the second row, first column ( $c_{21}$ ).
Multiply the second row of $A$ by the first column of $B$ :
$c_{21} = (0)(1) + (3)(3) + (2)(-1)$ $c_{21} = 0 + 9 - 2 = 7$
Calculate the element in the second row, second column ( $c_{22}$ ).
Multiply the second row of $A$ by the second column of $B$ :
$c_{22} = (0)(0) + (3)(-1) + (2)(2)$ $c_{22} = 0 - 3 + 4 = 1$
Form the product matrix $AB$ .
$AB = \begin{bmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{bmatrix} = \begin{bmatrix} 6 & -3 \\ 7 & 1 \end{bmatrix}$
The product $AB$ is $\boxed{\begin{bmatrix} 6 & -3 \\ 7 & 1 \end{bmatrix}}$ .

Multiply matrices A and B, where A = [[2, 1, -1], [0, 3, 2]] and B = [[1, 0], [3, -1], [-1, 2]].