How to Multiply Matrices Using Matrix Multiplication

Description

This video explains the difference between addition/subtraction and multiplication of matrices. It also explains why there is such a difference. Several example problems are provided in the video, along with a clear explanation of the multiplication process.

Overview

Matrix multiplication is very different from addition and subtraction with matrices. Instead of combining the numbers from the same places, you must combine rows from the first matrix with columns from the second matrix. When you are looking for the number for the top left corner – the first number of your matrix – you will look at the top row of the first matrix and the first column of the second matrix. Say you have 2 matrices like this:

{a  b} * {w x}

{c  d} * {y  z}

You will look at a and b, and w and y, to find your first term. The first number of your new matrix will be [(a * w) + (b * y)]. When you want to find the second term – the term still in the first row, but in a different column – you will switch you focus to the other column, while keeping your row of focus the same, and solve it in the same way. This must be done for every term in the matrices.