Matrix Multiplication

Before attempting matrix multiplication, makes sure you know the basics first.

The key to answering this question is to look at the dimensions of each matrix. Remember, they are always listed as row x column.

To see if the operation is defined, list the two dimensions next to each other. Important Note: The order does matter!

Next, check to see if the middle numbers are the same!

	Example #1	Example #2

Once the matrix multiplication is defined, you can find the dimensions of the result (the answer). The outside numbers will give you the new dimensions.

For the examples above, the results would be (2 x 3) and (3 x 1).

Here are more examples:

Now that you know how to determine the dimensions of the resulting matrix, now you need to know how to actually multiply them.

Example:

We are multiplying a (2 x 2)(2 x 2) - so the result will also be a (2 x 2).

You will need to multiply each corresponding row times the corresponding column - notice the circles below. Once you multiply the matching pieces, add the results.

It might seem a little confusing at first, but after a little practice you will get it. Of course, you might prefer to use the zipper method instead...

Now you are going to "zip" in the numbers that line up. Look at the light blue arrows, as well as the colored circles...

So, now that you have seen both methods of matrix multiplication, which do you prefer: the turn and flip method or the zipper method?

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