b Use matrix multiplication. Be careful with the order.
A
aRegistration fees:
165& 110 & 239
Number of students: 35& 28 32& 17 18& 12
B
bAerobics: $13 597 Step aerobics: $9358
Practice makes perfect
a Let's first copy the information about the number of students from the given table to a 3* 2 matrix.
35& 28 32& 17 18& 12
We now have to decide whether we will use a 3* 1 or a 1* 3 matrix for the registration fees.
To help the decision, let's look at the definition of matrix multiplication.
We already have the number of students stored in a 3* 2 matrix, so choosing a 1* 3 form for the registration fees allows us to multiply the two matrices.
Next, we need to decide the order of the numbers in the registration fee matrix.
Since the columns in the registration fee matrix (A) correspond to the rows of the matrix storing the number of students (B), let's use the same order.
Class-by-class
11 -class pass
Unlimited pass
We get the following matrix of the registration fees.
165& 110 & 239
b To find the total amount of money the gym received, let's multiply the two matrices we got in Part A. Note that the product can only be found if we put the registration fee matrix first.
Let's interpret the result we got. It is a 1* 2 matrix, and both elements are sums of products of elements in the two matrices. Let's see the details of the calculation of the first element.
The product of 165 and 35 is the product of the class-by-class registration fee and the number of people registered for class-by-class aerobics. Hence, 165(35) is the income from class-by-class aerobics registration.
Similarly, 110(32) is the income from 11-day aerobics passes, and 239(18) is the income from unlimited aerobics passes.
The sum of these is hence the income from aerobics registration.
Similarly, the second element of the result matrix is the income from step aerobics registration.
The gym received $13 597 from aerobics registration, and $9358 from step aerobics registration.
Extra
Using the calculator
To work out the product matrix with the calculator, we need to store the matrices in the memory.
Begin by pushing the 2ND button, followed by x^(-1) to access the matrix menu. Then, scroll to the right until you reach the EDIT menu and choose to edit any of the matrices.
Once matrix A containing the registration fees is stored, repeat the process to store the number of students in matrix B.
Now that the matrices are stored, you can access them through the NAMES option of the matrix menu.
Note that you can also see the dimensions of the stored matrices in the menu.
Using the names of the stored matrices on the calculator, the product matrix can be calculated in one step.
