﻿ Matrices Worksheets | Problems & Solutions

# Matrices Worksheets

Matrices Worksheets
• Page 1
1.
Which of the following is a column matrix?
 a. $\left(\begin{array}{c}9\\ 7\\ 7\end{array}\right)$ b. c. $\left(\begin{array}{ccc}- 4& 4& 0\end{array}\right)$ d.

#### Solution:

A matrix which has only one column is called a column matrix.

As (977) has 3 rows and 1 column, it is a column matrix.

2.
Which of the following is an identity matrix?
 a. $\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$ b. $\left(\begin{array}{cc}1& 1\\ 1& 1\end{array}\right)$ c. $\left(\begin{array}{cc}3& 6\\ 7& 5\end{array}\right)$ d. $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$

#### Solution:

Identity matrix is a square matrix with 1′s along the main diagonal (from the upper left corner to the lower right corner) and 0′s in all other positions

So, (1001) is the identity matrix.

3.
The table shows the data about three hockey teams A, B and C. Identify a matrix that displays the data as a 3 × 3 matrix.
 Win Draw Loss Team A 9 6 4 Team B 6 6 7 Team C 8 5 6

a.
 A B C WDL $\left(\begin{array}{ccc}9& 6& 8\\ 6& 6& 5\\ 4& 7& 6\end{array}\right)$
b.
 A B C WDL $\left(\begin{array}{ccc}9& 6& 4\\ 6& 6& 7\\ 8& 5& 6\end{array}\right)$
c.
 A B C WDL $\left(\begin{array}{ccc}6& 9& 8\\ 6& 5& 6\\ 4& 6& 7\end{array}\right)$
d.
None of the above

#### Solution:

Use Win(W), Draw(D), Loss(L) for the rows and Team A, Team B, Team C for the columns.

 A B C WDL (968665476)

4.
Choose the matrix which shows the information about admissions in a college.
Admitted (A) : Boys 341, Girls 291.
Rejected (R): Boys 133, Girls 113.
a.
 B G AR $\left(\begin{array}{cc}133& 113\\ 341& 291\end{array}\right)$
b.
 B G AR $\left(\begin{array}{cc}341& 113\\ 291& 133\end{array}\right)$
c.
 B G AR $\left(\begin{array}{cc}133& 341\\ 113& 291\end{array}\right)$
d.
 B G AR $\left(\begin{array}{cc}341& 291\\ 133& 113\end{array}\right)$

#### Solution:

Use Admitted (A) and Rejected ( R ) for the rows and Boys (B), Girls (G) for the columns.

 B G AR (341291133113)

5.
Choose the matrix which shows the information about the number of movies screened in three months at two locations.
Location 1 (L1): March 3, April 5, and May 2.
Location 2 (L2): March 2, April 6, and May 2.
a.
 March April May L1L2
b.
 March April May L1L2
c.
 March April May L1L2
d.
 March April L1L2

#### Solution:

Use Location 1 (L1) and Location 2 (L2) for the rows and months for the columns.

6.
A business school conducted a survey of companies in its state. They mailed questionnaire to different companies. Choose the matrix which shows the information.
Small companies (S) : Response 240, No Response 160.
Medium sized companies (M): Response 200, No Response 200.
Large companies (L) : Response 320, No Response 80.
a.
 R NR SML $\left(\begin{array}{cc}240& 160\\ 320& 80\\ 200& 200\end{array}\right)$
b.
 R NR SML $\left(\begin{array}{cc}200& 80\\ 160& 200\\ 240& 320\end{array}\right)$
c.
 R NR SML $\left(\begin{array}{cc}320& 80\\ 200& 200\\ 240& 160\end{array}\right)$
d.
 R NR SML $\left(\begin{array}{cc}240& 160\\ 200& 200\\ 320& 80\end{array}\right)$

#### Solution:

Use Small companies (S), Medium-sized companies (M), Large companies (L) for the rows and Response (R), No response (NR) for the columns.

The matrix form is:
 R NR SML (24016020020032080)

7.
Choose the matrix which shows the information about the number of animals.
Zoo - A: Monkeys 9, Tigers 9.
Zoo - B: Monkeys 6, Tigers 6.
Zoo - C: Monkeys 3, Tigers 3.
a.
 M T ABC $\left(\begin{array}{cc}9& 9\\ 6& 6\\ 3& 3\end{array}\right)$
b.
 M T ABC $\left(\begin{array}{cc}3& 3\\ 6& 6\\ 9& 9\end{array}\right)$
c.
 M T ABC $\left(\begin{array}{cc}3& 3\\ 9& 9\\ 6& 6\end{array}\right)$
d.
 M T ABC $\left(\begin{array}{cc}9& 9\\ 6& 6\\ 3& 3\end{array}\right)$

#### Solution:

Use Zoo - A, Zoo - B, Zoo - C for the rows and Monkeys (M), Tigers (T) for the columns.

The matrix form is:
 M T ABC (996633)

8.
Represent the following data in a matrix.
Library - A: Books 3068, Journals 14, CDs 225
Library - B: Books 3082, Journals 45, CDs 798
a.
 Library A Library B BooksJournalsCds
b.
 Library A Library B BooksJournalsCds
c.
 Library A Library B BooksJournalsCds
d.
None of the above

#### Solution:

The matrix form is:
 Library A Library B BooksJournalsCds (3068    308214    45225    798)

9.
Choose the matrix which shows the information about the number of items sold per day by two stores:
Store A: TVs 13, DVD Players 21, Refrigerators 5.
Store B: TVs 8, DVD Players 36, Refrigerators 7.
a.
 T D R AB $\left(\begin{array}{ccc}5& 21& 13\\ 7& 36& 8\end{array}\right)$
b.
 T D R AB $\left(\begin{array}{ccc}13& 5& 21\\ 8& 7& 36\end{array}\right)$
c.
 T D R AB $\left(\begin{array}{ccc}13& 21& 5\\ 8& 36& 7\end{array}\right)$
d.
 T D R AB $\left(\begin{array}{ccc}7& 36& 8\\ 5& 21& 13\end{array}\right)$

#### Solution:

Use store A, store B for the rows and TVs (T), DVD Players(D), Refrigerators (R) for the columns.

The matrix form is:
 T D R AB (132158367)

10.
Choose the matrix which shows the test scores of three students A, B and C.

A : Zoology 8, Geography 11, History 13, Economics 18.
B : Zoology 11, Geography 13, History 15, Economics 20.
C : Zoology 15, Geography 13, History 18, Economics 23.
a.
 Z G H E ABC $\left(\begin{array}{cccc}8& 11& 13& 18\\ 11& 13& 15& 20\\ 15& 13& 18& 23\end{array}\right)$
b.
 Z G H E ABC $\left(\begin{array}{cccc}11& 11& 13& 18\\ 8& 13& 15& 20\\ 15& 13& 18& 23\end{array}\right)$
c.
 Z G H E ABC $\left(\begin{array}{cccc}8& 11& 13& 23\\ 11& 13& 15& 23\\ 15& 13& 18& 23\end{array}\right)$
d.
None of the above

#### Solution:

Use A, B, C for the rows and Zoology (Z), Geography (G), History (H), Economics (E) for the columns.

The matrix form is:
 Z G H E ABC (81113181113152015131823)