How do you multiply matrices?
In this video we’re talking about everything you need to know about matrix multiplication. We’ll start simple and look at what it means to multiply a matrix by a scalar, and then move on to multiplying matrices together using the dot product, and a special trick for remembering how to do matrix multiplication.
We’ll cover rules of algebra for matrices, including commutative, associative, and distributive properties, and show that each of these properties applies to matrix multiplication, except for the commutative property.
We’ll talk about matrix dimensions and how to describe a matrix by its rows and columns. We’ll address the fact that not all matrix multiplication is defined, and that you in fact need the number of columns in the first matrix to match the number of rows in the second matrix in order for the multiplication to work at all. You can also use matrix dimensions to figure out the dimensions of the resulting matrix after the multiplication.
Finally, we’ll look at identity matrices and zero matrices, which act like the special numbers 1 and 0 when it comes to matrix multiplication.
0:17 // Multiplying a matrix by a scalar
0:37 // Applying algebra to matrices
0:44 // Matrix multiplication is not commutative
1:21 // Associative property and distributive property with matrices
2:00 // Matrix dimensions
2:21 // Which matrices can be multiplied together?
2:55 // How to figure out whether matrices can be multiplied together. How to figure out the dimensions of the resulting matrix.
3:40 // How to multiply matrices using the dot product
4:26 // How to remember what to put where
5:16 // Identity matrices
5:51 // Multiplying by the identity matrix is like multiplying by 1
6:31 // Multiplicative inverses
6:56 // Zero matrices
7:23 // Summary