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Chapter 4: Q46. (page 181)

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

A2脳3路B3脳2

Short Answer

Expert verified

Matrix product of given matrices is defined.

Product matrix has 2 rows and 2 columns.

Step by step solution

01

- Write condition for matrix product to be defined.

For two matrices A and B, the product A路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 3 columns and matrix B has 3 rows and 2 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路B has 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 2 columns.

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