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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