Chapter 4, Problem 16MCQ

To determine

Tofind:whether the matrix product is defined or not and state the dimension of the product.

Answer to Problem 16MCQ

The dimension of the product matrix will be $2\times 2$ .

Explanation of Solution

Given:

  ${\text{A}}_{\text{2×3}}{\text{.B}}_{\text{3×2}}$ .

Concept used:

To multiply the two matrices column of the first matrices must equals to the raw of the second Matrices.

The product will be defined. The dimension of the product of two matrices can be known taking Raw of the first matrix and taking the column of the second matrix.

Calculation:

Here ${\text{A}}_{\text{2×3}}{\text{.B}}_{\text{3×2}}$ .

Two multiply the two matrices column of the first matrices must equals to the raw of the second matrices.

Since column of first matrix $=3$ and the row of second matrix $=3$ .

So, the product will be defined. The dimension of the product of two matrices can be known taking the raw of the first matrix and taking the column of the second matrix.

Or outer dimension will be taken as product of the matrices.

Hence the dimension of the product matrix will be $2\times 2$ .