The key to multiplying correctly is to make sure the number of columns in the first matrix matches the number of rows in the second matrix. Not only does the number need to match, but what that number represents must also match. The example about half way through the video below illustrates this idea.

- Video: Matrix Multiplication

Now let’s look at what the students did in class…look for where they match up the numbers in their work.

**Problem 1** A political candidate plans to use three methods of advertising: newspapers, radio, and cable TV. The cost per ad (in thousands of dollars) for each type of media is given by matrix A. Matrix B shows the number of ads per month in these three media that are targeted to single people, to married males aged 35 to 55, and to married females over 65 years of age. Find the matrix that gives the cost of ads for each target group.

Since the cost matrix A is in thousands of dollars, the product entries are in thousands of dollars also. The columns in the first matrix represent the different types of ads as does the rows in the second matrix.

**Problem 2** Men and women in a church choir wear choir robes in the sizes shown in matrix A. Matrix B contains the prices (in dollars) of new robes and hoods according to size. Find the matrix that gives the total cost of robes and hoods for men and women.

Note that the columns in B represent sizes (S, M, L) and the rows in A do too. So BA is the appropriate matrix product to compute.