Chapter 4.4, Problem 74E

Test averages. A teacher has given four tests to a class of five students and stored the results in the following matrix:

Tests

$\begin{array}{l}\begin{array}{ccccc}& 1& 2& 3& 4\end{array}\\ \begin{array}{c}\text{Ann}\\ \text{Bob}\\ \text{Carol}\\ \text{Dan}\\ \text{Eric}\end{array}\left[\begin{array}{cccc}78& 84& 81& 86\\ 91& 65& 84& 92\\ 95& 90& 92& 91\\ 75& 82& 87& 91\\ 83& 88& 81& 76\end{array}\right]=M\end{array}$

Discuss methods of matrix multiplication that the teacher can use to obtain the information indicated below. In each case, state the matrices to be used and then perform the necessary operations.

(A) The average on all four tests for each student, assuming that all four tests are given equal weight.

(B) The average on all four tests for each student, assuming that the first three tests are given equal weight and the fourth is given twice this weight.

(C) The class average on each of the four tests.