FURMATH EXAM 1: Matrices and Vector Spaces, Exams of Linear Algebra

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MATRICES 2013

MULTIPLE CHOICE

REVISION

SECTION B – Module 6: Matrices – continued

Question 1

The matrix below shows the airfares (in dollars) that are charged by Zeniff Airlines to fly between

Adelaide ( A ), Melbourne ( M ) and Sydney ( S ).

from

A M S

A

M to

S

7KHFRVWWRÀ\IURP0HOERXUQHWR6\GQH\ZLWK=HQLII$LUOLQHVLV

A. $

B. $

C. $

D. $

E. $

Question 2

If A =

⎥ ,^ B^ =^

⎥ and^ C^ =^

⎥ , then^ AB^ + 2 C^ equals

A.

B.

C.

D.

E.

Module 6: Matrices

Before answering these questions you must shade the Matrices box on the answer sheet for

multiple-choice questions and write the name of the module in the box provided.

SECTION B – Module 6: Matrices – continued

Use the following information to answer Questions 5 and 6.

Two politicians, Rob and Anna, are the only candidates for a forthcoming election. At the beginning of the

election campaign, people were asked for whom they planned to vote. The numbers were as follows.

Candidate Number of people who plan

to vote for the candidate

Rob 5692

Anna 3450

During the election campaign, it is expected that people may change the candidate that they plan to vote for

each week according to the following transition diagram.

Rob Anna

Question 5

The total number of people who are expected to change the candidate that they plan to vote for one week after

the election campaign begins is

A. 828

B. 1423

C. 2251

D. 4269

E. 6891

Question 6

The election campaign will run for ten weeks.

If people continue to follow this pattern of changing the candidate they plan to vote for, the expected winner

after ten weeks will be

A. Rob by about 50 votes.

B. Rob by about 100 votes.

C. Rob by fewer than 10 votes.

D. Anna by about 100 votes.

E. Anna by about 200 votes.

35  )850$7+(;$0

6(&7,21%±0RGXOH0DWULFHV ±FRQWLQXHG

4XHVWLRQ

(DFKQLJKWDODUJHJURXSRIPRXQWDLQJRDWVVOHHSDWRQHRIWZRORFDWLRQV A RU B 

2QWKH¿UVWQLJKWHTXDOQXPEHUVRIJRDWVDUHREVHUYHGWREHVOHHSLQJDWHDFKORFDWLRQ

)URPQLJKWWRQLJKWJRDWVFKDQJHWKHLUVOHHSLQJORFDWLRQVDFFRUGLQJWRDWUDQVLWLRQPDWUL[ T 

,WLVH[SHFWHGWKDWLQWKHORQJWHUPPRUHJRDWVZLOOVOHHSDWORFDWLRQ A WKDQDWORFDWLRQ B 

$VVXPLQJWKHWRWDOQXPEHURIJRDWVUHPDLQVFRQVWDQWDWUDQVLWLRQPDWUL[ T WKDWZRXOGSUHGLFWWKLVRXWFRPHLV

this night

A B

A

B

T= next night

this night

A B

A

B

T= next night

this night

A B

A

B

T= next night

this night

A B

A

B

T= next night

this night

A B

A

B

T= next night

SECTION B – Module 6: Matrices – continued

Question 1

The order of the matrix

is

A. 2 × 2

B. 2 × 3

C. 3 × 2

D. 4

E. 6

Question 2

Peter bought only apples and bananas from his local fruit shop.

The matrix

A B

N = [3 4]

lists the number of apples ( A ) and bananas ( B ) that Peter bought.

The matrix

C

A

B

lists the cost (in dollars) of one apple and one banana respectively.

The matrix product, NC , gives

A. the total amount spent by Peter on the fruit that he bought.

B. the total number of pieces of fruit that Peter bought.

C. the individual amounts that Peter spent on apples and bananas respectively.

D. the total number of pieces of fruit that Peter bought and the total amount that he spent.

E. the individual number of apples and bananas that Peter bought and the individual amounts that Peter spent

on these apples and bananas respectively.

Module 6: Matrices

Before answering these questions you must shade the Matrices box on the answer sheet for multiple-

choice questions and write the name of the module in the box provided.

SECTION B – Module 6: Matrices – continued

TURN OVER

Question 3

The total cost of one ice cream and three soft drinks at Catherine’s shop is $9.

The total cost of two ice creams and five soft drinks is $16.

Let x be the cost of an ice cream and y be the cost of a soft drink.

The matrix

x

y

is equal to

A.

x

y

B.

C.

D.

E.

SECTION B – Module 6: Matrices – continued

TURN OVER

Question 5

A system of three simultaneous linear equations is written in matrix form as follows.

x

y

z

One of the three linear equations is

A. x – 2 y + z = 4

B. x + y + 3 z = 11

C. 2 x – y = –

D x + 3 z = 11

E. 3 y – z = –

SECTION B – Module 6: Matrices – continued

Question 6

Vince, Nev and Rani all service office equipment.

The matrix T shows the time that it takes (in minutes) for each of Vince ( V ), Nev ( N ) and Rani ( R ) to service

a photocopier ( P ), a fax machine ( F ) and a scanner ( S ).

V N R

T

P

F

S

The matrix U below displays the number of photocopiers, fax machines and scanners to be serviced in three

schools, Alton ( A ), Borton ( B ) and Carlon ( C ).

P F S

U

A

B

C

A matrix that displays the time that it would take each of Vince, Nev and Rani, working alone, to service the

photocopiers, fax machines and scanners in each of the three schools is

A.

B.

C.

D.

E.

END OF MULTIPLE-CHOICE QUESTION BOOK

Question 9

Robbie completed a test of four multiple-choice questions.

Each question had four alternatives, A , B , C or D.

Robbie randomly guessed the answer to the first question.

He then determined his answers to the remaining three questions by following the transition matrix

this question

A B C D

T

A

B

C

D

 next

qquestion

Which of the following statements is true?

A. It is impossible for Robbie to give the same answer to all four questions.

B. Robbie would always give the same answer to the first and fourth questions.

C. Robbie would always give the same answer to the second and third questions.

D. If Robbie answered A for question one, he would have answered B for question two.

E. It is possible that Robbie gave the same answer to exactly three of the four questions.

SECTION B – Module 6: Matrices – continued

TURN OVER

Question 1

equals

A.

B. 6

C.

D.^5

E.

Question 2

The matrix

can also be written as

A. [12 15 3] + [–6 0 24]

B.

C.

D.

s 

E. 3

s 

Module 6: Matrices

Before answering these questions you must shade the Matrices box on the answer sheet for multiple-

choice questions and write the name of the module in the box provided.

SECTION B – Module 6: Matrices – continued

TURN OVER

Question 5

A , B , C , D and E are five intersections joined by roads as shown in the diagram below.

Some of these roads are one-way only.

A B

D C

E

The matrix below indicates the direction that cars can travel along each of these roads.

In this matrix

• 1 in column A and row B indicates that cars can travel directly from A to B
• 0 in column B and row A indicates that cars cannot travel directly from B to A (either it is a one-way road

or no road exists).

from intersection

A B C D E

A

B

C

D

E

to intersection

Cars can travel in both directions between intersections

A. A and D

B. B and C

C. C and D

D. D and E

E. C and E

SECTION B – Module 6: Matrices – continued

Question 6

T is a transition matrix, where

from

to

P Q

T

P

Q

An equivalent transition diagram, with proportions expressed as percentages, is

A.

P Q

B.

P Q

C.

P Q

E.

P Q

D.

P Q

SECTION B – Module 6: Matrices – continued

TURN OVER

Question 1

If

d

then d is equal to

A. –

B. –

C. 7

D. 10

E. 11

Question 2

Apples cost $3.50 per kg, bananas cost $4.20 per kg and carrots cost $1.89 per kg.

Ashley buys 3 kg of apples, 2 kg of bananas and 1 kg of carrots.

A matrix product to calculate the total cost of these items is

A. 3

B. [3 2 1] [3.50 4.20 1.89]

C. [3.50 × 2 4.20 × 3 1.89 × 1]

D. 3

[.^.^. ]

E.

[.^.^. ]

Module 6: Matrices

Before answering these questions you must shade the Matrices box on the answer sheet for multiple-

choice questions and write the name of the module in the box provided.

SECTION B – Module 6: Matrices – continued

Question 3

The cost prices of three different electrical items in a store are $230, $290 and $310 respectively.

The selling price of each of these three electrical items is 1.3 times the cost price plus a commission of $20 for

the salesman.

A matrix that lists the selling price of each of these three electrical items is determined by evaluating

A.

. × 20

• [ ]

B.

. × 1 3. × 20

C.

. ×

D.

. ×. ×

E.

. ×

Question 4

Matrix A is a 1 × 3 matrix.

Matrix B is a 3 × 1 matrix.

Which one of the following matrix expressions involving A and B is defined?

A. A +

B

B. 2 B × 3 A

C. A

2 B

D. B

E. B − A

Question 5

The determinant of

6 x

⎥ is equal to 9.

The value of x is

A. –

B. –4.

C. 1

D. 4.

E. 7