Chapter 4, Problem 5MCQ

(a)

To determine

To find: The matrix for the sale of each week.

Answer to Problem 5MCQ

The matrix for the first week is $W_1=\left[\begin{array}{cccc}25& 14& 18& 5\\ 44& 10& 13& 8\end{array}\right]$ and the matrix for the second week is $W_2=\left[\begin{array}{cccc}32& 26& 15& 4\\ 18& 38& 17& 2\end{array}\right]$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Grade	Week	T-shirt	Sweatshirt	Hat	Coat
9	1	25	14	18	5
9	2	32	26	15	4
10	44	10	13	8
10	2	18	38	17	2

Table 1

Calculation:

From the Table 1, the matrix for the first week is,

  $W_1=\left[\begin{array}{cccc}25& 14& 18& 5\\ 44& 10& 13& 8\end{array}\right]$

From the Table 1, the matrix for the second week is,

  $W_2=\left[\begin{array}{cccc}32& 26& 15& 4\\ 18& 38& 17& 2\end{array}\right]$

(b)

To determine

To find: The matrix for the two week sale.

Answer to Problem 5MCQ

The matrix for the two week sale is $\left[\begin{array}{cccc}57& 40& 33& 9\\ 62& 48& 30& 10\end{array}\right]$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Grade	Week	T-shirt	Sweatshirt	Hat	Coat
9	1	25	14	18	5
9	2	32	26	15	4
10	44	10	13	8
10	2	18	38	17	2

Table 1

Calculation:

From the Table 1, the matrix for the first week is,

  $W_1=\left[\begin{array}{cccc}25& 14& 18& 5\\ 44& 10& 13& 8\end{array}\right]$

From the Table 1, the matrix for the second week is,

  $W_2=\left[\begin{array}{cccc}32& 26& 15& 4\\ 18& 38& 17& 2\end{array}\right]$

Then, the matrix for the two week sale is.

  $\begin{array}{c}{W}_1=\left[\begin{array}{cccc}25& 14& 18& 5\\ 44& 10& 13& 8\end{array}\right]+\left[\begin{array}{cccc}32& 26& 15& 4\\ 18& 38& 17& 2\end{array}\right]\\ =\left[\begin{array}{cccc}57& 40& 33& 9\\ 62& 48& 30& 10\end{array}\right]\end{array}$