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PAGE: 200SET: ExercisesPROBLEM: 46
Please look in your text book for this problem Statement

 

Multiplication of two matrices is possible if the number of columns in the

first matrix equals the number of rows in the second matrix.

Let A be the first matrix and B be the second matrix.

The dimensions of the first matrix A are , so the number of the columns

in the first matrix is 2.

The dimensions of the second matrix B are , so the number of the rows

in the second matrix B is 2.

The number of columns in the first matrix equals the number of rows in the

second matrix. So, matrix product is possible and its dimensions are .

Let P be the matrix product.

The matrix P is

The element  of the matrix () is the sum of the products

of the corresponding elements in the i th row of the first matrix

() and column j th column of the second matrix ().

 where is the row index and .

Find the element .

The element is the sum of the products of the corresponding elements

of row 1 of the matrix A and column 1 of the second matrix..

Next find the element .

The element is the sum of the products of the corresponding elements

of row 1 of the matrix A and column 2 of the second matrix..

Next find the element .

The element is the sum of the products of the corresponding elements

of row 2 of the matrix A and column 1 of the second matrix.

Next find the element .

The element is the sum of the products of the corresponding elements

of row 2 of the matrix A and column 2 of the second matrix.

Simplify the product matrix.

The product matrix is .



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