Math

MT132 (M132): Linear Algebra

Tutor Marked Assignment

Cut-Off Date: November --, 2020 Total Marks: 40

Contents

Feedback form ……….……………..…………..…………………….…...….. 2

Question 1 ……………………..………………………………………..……… 3

Question 2 ……………………………..………………..……………………… 4

Question 3 ………………………………..………………..…………………… 5

Question 4 ………………..……………………………………..……………… 6

Plagiarism Warning:

As per AOU rules and regulations, all students are required to submit their own TMA work and avoid plagiarism. The AOU has implemented sophisticated techniques for plagiarism detection. You must provide all references in case you use and quote another person's work in your TMA. You will be penalized for any act of plagiarism as per the AOU's rules and regulations.

Declaration of No Plagiarism by Student (to be signed and submitted by students with TMA work):

I hereby declare that this submitted TMA work is a result of my own efforts and I have not plagiarized any other person's work. I have provided all references of information that I have used and quoted in my TMA work.

Student Name : _____________________

Signature : _________________

Date : ___________

MT132 TMA Feedback Form

[A] Student Component

Student Name : ____________________

Student Number : ____________

Group Number : _______

[B] Tutor Component

	Comments	Weight	Mark
Q_1		10
Q_2		10
Q_3		10
Q_4		10
		40

General Comments:
	Tutor name:

The TMA covers only chapters 1 and 2. It consists of four questions; each question is worth 10 marks. Please solve each question in the space provided. You should give the details of your solutions and not just the final results.

Q−1: [5×2 marks] Answer each of the following as True or False justifying your answers:

a) Let and . If , then .

b) If and , then .

c) If is a non-singular matrix, then .

d) .

e) The vector is a linear combination of the vectors and .

Q−2: [5+5 marks]

a) Let .

i. Find all values of , if any, for which exists

ii. For solve the system .

b) Solve for : .

Q−3: [5+5 marks]

a) Solve the linear system .

b) Consider the linear system:

For which values of does the linear system have

i. no solution;

ii. a unique solution;

iii. infinitely many solutions.

Q−4: [5+5 marks] Let be a linearly independent a set of vectors in and be a set of vectors in , where , and .

a) Determine whether the set is linearly independent.

b) If possible, write each of the vectors , and as a linear combination of vectors in .

MT132 – Linear Algebra 2020-2021 / Fall

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