Matrix Multiplication

Definition of Matrix Multiplication

1. When the number of columns in matrix is equal to the number of rows in matrix , the product of and is a matrix where each element in the -th row and -th column is obtained by multiplying the corresponding elements of the -th row of and the -th column of , and then summing the products. This product is denoted by .
   
   
2. If matrix is an matrix and matrix is an matrix, the product matrix will be an matrix:

Methods for Calculating Matrix Products

1. For a matrix multiplied by a matrix:
   
2. For a matrix multiplied by a matrix:
3. For a matrix multiplied by a matrix:
4. For a matrix multiplied by a matrix:
5. For a matrix multiplied by another matrix:

Example 1. Calculate the following:

 Solution

Example. 2
Calculate the following:

 Solution

Example. 3 Calculate the following:

 Solution

Example. 4 Calculate the following:

 Solution