When multiplying matrices, you first need to look at the dimensions
of both matrices. The term dimension refers to the size of the
matrix. The first number represents the number of rows in the
matrix and the second number refers to the number of columns.
Therefore, a 2x5 matrix would have two rows and five columns.
When multiplying matrices, first you need to make sure that the
dimension of the columns (vertical) in the first matrix is the
same as the dimension of the rows (horizontal) in the second matrix.
If they are not the same, then the two matrices cannot be multiplied.
For this lesson, we will focus on multiplying with two matrices.
If you put the dimensions of the first matrix next to the dimensions
of the second matrix (2x3) (3x2), the two middle numbers must
be the same in order to multiply, and the two numbers on the outside
ends will be the dimensions of the product matrix.
Now that you know you can multiply the two matrices,
it’s time to do the math. For you to do this, you have to
multiply all the numbers in the first row of the first matrix by
all the numbers in the first column, and any others that follow,
of the second matrix. Then you multiply the numbers in the second
row of the first matrix by all the numbers in the first column,
and any others that follow, of the second matrix. Once you are done
multiplying, you must add the products together. An example of the
correct way to do this is shown below:
An easy way to do this without confusing which numbers
to multiply by which row or column is to use your fingers or a piece
of card size paper to cover the rows and columns that are not being
multiplied. This way you can only see the row and column that you
are multiplying, which makes the process easier and less confusing. |
