Exercise 5 Question #5

The Question:

Winners at a science fair are determined by a scoring system based on five items with different weights attached to each item. The items and associated weights are the summary of background research- weight 3; experimental procedure- weight 5; research paper- weight 6; project display- weight 8; and, creativity of idea- weight 4. Each project is judge by grading each of the five items on a scale from 0-10, with 10 being the highest. The total score for a project is derived by adding the products of the corresponding weights and points for each item.

a) Create a 1x5 matrix giving the weights of each item. Label it A.

b) Create a 5x7 matrix to show the number of points gained by each contestant. Label it B.

c) What does the matrix product AB indicate?

d) Calculate AB and record it. Summarize the results of the science fair.

How you get there:

a) [3 5 6 8 4]

We arrived at this answer by looking back at the question, and using the weight numbers provided there.

b)

This table is given to you in the question so all you have to do is copy it.

c) The matrix product of AB indicates that it is a 1x7 representing the overall score each person received.

You can arrive at 1x7 by taking the dimensions of the matrix A and matrix B,

[A]=1x5 5x7=[B]

the outer dimensions show what size the answer will be, and the inner show you can multiply it.

d) [A] [B]= [223 231 227 229 220 216 228]

This is done simply by entering in the two matricies into your graphing calculator and multiplying them together in this order. If you multiply [B] [A] it does not work, you will get a totally wrong answer.

The results of the science fair are as follows:

First Place- Jane 231

Second- Kathy 229

Third- Terri 228

Fourth- Bryan 227

Fifth- Peter 223

Sixth- Mary 220

Last Place- Chris 216