with matrices is not too difficult once you get in the routine of performing the process. You can practice more problems like those above on the accompanying worksheet.
A second type of multiplication is to multiply two matrices together and it is a little more involved.
Multiplication of matrices has different rules than addition and subtraction. For matrix
multiplication, the columns of the first matrix
MUST match with the rows of the second matrix.
A = and B = .
To multiply AB, we first have to make sure that the number of columns in A is the same as the number of rows in B. Matrix
A has 2 columns and matrix
B has 2 rows so we will be able to perform this operation. The dimension of the new matrix
will be defined as:
Rows = number of rows in A
Columns = number of columns in B
An easier way to look at these dimensions is shown in the following figure:
Let’s do the multiplication and call our new matrix
M (AB = M). This matrix
will be a
. We simply need to fill in the six entries in this matrix.
Remember we are working with the matrices A and B shown below.
A = and B = .
We begin by multiplying (4)(2) and adding that to (6)(–2). That is now the entry
Now multiply (4)( –3) and add that to (6)(0). This is the entry
Multiply (4)(1) and add that to (6)(5). This is the entry
We now have the top row of our answer matrix
We’ll follow the same process to fill in the second row of the answer matrix.
Entry for m21 = (1)(2) + (9)( –2)
Entry for m22 = (1)( –3) + (9)(0)
Entry for m23 = (1)(1) + (9)(5)
The answer matrix
operations look like this:
M = Matrix
M simplifies to:
AB = M =
Notice that if you were to try to do BA, you could not because the dimensions would not match up. Always check your dimensions before beginning any multiplication!