In a
previous blog post, we talked about one type of multiplication for matrices, scalar multiplication. In this blog post be will talk about the other type of multiplication for matrices, matrix multiplication.
Matrix multiplication is when you multiply matrix A, an n x m matrix, by matrix B, an m x p matrix, to get their product, matrix C, and n x p matrix. This means you can only multiply matrices, where matrix A has the same amount of columns as there are rows in matrix B.
In order to multiply matrices, we will have to calculate the dot product of the rows of the first matrix, matrix A, and the columns of the second matrix, matrix B.
Let’s see what this looks like:
In words, what we are seeing is the dot product of the first row of matrix A and the first column of matrix B make an element in the 1st row and 1st column of their product. The dot product of the second row of matrix A and the first column of matrix B make an element in the 2nd row and 1st column. The dot product of the first row of matrix A and the second column of matrix B make an element in the 1st row and 2nd column. And so on . . .
Now, let’s see some examples to help better understand how multiply matrices.
First example (
click here):
1. Take the dot product of the rows of matrix A and the columns of matrix B
2. Simplify
Next example (
click here):
1. Take the dot product of the rows of matrix A and the columns of matrix B
2. Simplify
Last example (
click here):
1. Take the dot product of the rows of matrix A and the columns of matrix B
2. Simplify
Matrix multiplication can be difficult and tricky, when learning it for the first time. The more you practice it, the more it’ll become second nature to you. Check out Symbolab’s
Practice for practice problems and quizzes on this topic.
Until next time,
Leah
