Can you perform matrix multiplication for matrices A and B?

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution to the matrix multiplication problem:

We are given two matrices:

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

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

Determine the order (dimensions) of matrix $A$ .
Matrix $A$ has 2 rows and 3 columns. So, its order is $2 \times 3$ .
Determine the order (dimensions) of matrix $B$ .
Matrix $B$ has 2 rows and 3 columns. So, its order is $2 \times 3$ .
Check if matrix multiplication $AB$ is defined.
For matrix multiplication $AB$ to be defined, the number of columns in the first matrix ( $A$ ) must be equal to the number of rows in the second matrix ( $B$ ).
Number of columns in $A = 3$ .
Number of rows in $B = 2$ .
Since $3 \ne 2$ , the matrix multiplication $AB$ is not defined.

The multiplication of the given matrices is $\text{not defined}$ .

Answer