Chapter 7.2, Problem 65E

Solution

To find: The order of the product of two matrix, while the order of the matrix $A$ and $B$ is $3\times 2$ and $2\times 4$ .

A. $2\times 2$

B. $3\times 4$

C. $4\times 3$

D. $6\times 8$

E. The product is not defined.

The correct match is option (B).

Given Information:

The order of the matrix $A$ and $B$ is $3\times 2$ and $2\times 4$ . The given options are defined as,

A. $2\times 2$

B. $3\times 4$

C. $4\times 3$

D. $6\times 8$

E. The product is not defined.

Explanation:

Consider the given matrix order,

To multiply the two matrix, the number of column of first matrix should be equal to the number of row of the second matrix. And the order of the obtained matrix will be the number of row of first matrix and the number of column of the second matrix.

In the multiplication of the matrix $A$ and $B$ , the order of $AB$ will be $3\times 4$

Hence, the correct option is (B) $3\times 4$ .