Algebra 2, 2008
46

 PAGE: 200 SET: Exercises PROBLEM: 46

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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