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Chapter 4: Q48. (page 181)

Determine whether each matrix product is defined. If so, state the dimensions of the product.

A2×5·B5×5

Short Answer

Expert verified

Matrix product of given matrices is defined.

Product matrix has 2 rows and 5 columns.

Step by step solution

01

- Write condition for matrix product to be defined.

For two matrices A and B, the product A·B is defined when number of columns of matrix A is equal to the number of rows of matrix B.

02

- Write dimensions of given matrices

Matrix A has 2 rows and 5 columns and matrix B has 5 rows and 5 columns.

03

- Check multiplication is defined or not

As, number of columns of matrix A is equal to the number of rows of matrix B.

So multiplication is defined.

04

- Write dimension of product matrix

When multiplication is defined then resultant matrix A·Bhas number of rows equal to the number of rows of matrix A and its number of column is equal to the number of columns of matrix B

So product of given two matrices gives a matrix which has 2 rows and 5 columns.

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