Chapter 3.5, Problem 12CYU

a.

To determine

To find: Matrix for the information from each test.

Answer to Problem 12CYU

Test-1 is $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]$

Test-2 is $\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

Explanation of Solution

Given equation:

Table shows the test grade for each student.

There are three students.

From the given table

We can write a matrix for the information from each test.

Rows represent each student as there are three students there will be three rows.

Columns represents Test.

As we are finding a matrix for each test there will be only one Column.

Therefore, from given table,

Matrix for Test-1 is

  $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]$

Matrix of Test-2 is

  $\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

b.

To determine

To find: Sum of the scores from the two tests expressed as a matrix.

Answer to Problem 12CYU

  $sum=\left[\begin{array}{c}157\\ 149\\ 179\end{array}\right]$

Explanation of Solution

Given equation:

Table shows the test grade for each student.

There are three students.

Test-1 is $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]$

Test-2 is $\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

Sum of matrices = $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]+\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

  $\begin{array}{l}\Rightarrow sum=\left[\begin{array}{c}85+72\\ 75+74\\ 96+83\end{array}\right]\\ \Rightarrow sum=\left[\begin{array}{c}157\\ 149\\ 179\end{array}\right]\end{array}$

c.

To determine

To find: Difference in scores from test-1 to test-2 as a matrix.

Answer to Problem 12CYU

  $difference=\left[\begin{array}{c}13\\ 1\\ 13\end{array}\right]$

Explanation of Solution

Given equation:

Table shows the test grade for each student.

There are three students.

Test-1 is $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]$

Test-2 is $\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

Difference of matrices = $\left[\begin{array}{c}85\\ 75\\ 96\end{array}\right]-\left[\begin{array}{c}72\\ 74\\ 83\end{array}\right]$

  $\begin{array}{l}\Rightarrow difference=\left[\begin{array}{c}85-72\\ 75-74\\ 96-83\end{array}\right]\\ \Rightarrow difference=\left[\begin{array}{c}13\\ 1\\ 13\end{array}\right]\end{array}$