Chapter 3.7, Problem 66SR

To determine

Whether the matrix product $A_{4\times 2}.B_{2\times 6}$ is defined. If so, state the dimension of the product.

Answer to Problem 66SR

The matrix product $A_{4\times 2}.B_{2\times 6}$ is defined of dimension $4\times 6$ .

Explanation of Solution

Given information :

Given matrix product $A_{4\times 2}.B_{2\times 6}$ .

The condition of existence of matrix product $A_{m\times n}.B_{p\times q}$ , is the number of columns of matrix $A$ is equals to the number of rows of matrix $B$ .

  $\Rightarrow n=p$

Thus, the inner dimensions are equal then the matrix product $A_{m\times n}.B_{p\times q}$ is defined and its dimension is equals to $m\times q$ .

Now consider given matrix product $A_{4\times 2}.B_{2\times 6}$ , $wherem=4,n=2,p=2,q=6.$

  $\Rightarrow n=p=2$

Thus, the inner dimensions are equal.

Hence, the matrix product $A_{4\times 2}.B_{2\times 6}$ is defined of dimension $4\times 6$ .