math Linear Algebra

MT132 (M132): Linear Algebra

Tutor Marked Assignment

Cut-Off Date: ---, 2018 Total Marks: 40

Contents

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

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

Question 2 ……………………………..………………..……………………… 3

Question 3 ………………………………..………………..…………………… 4

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

Plagiarism Warning:

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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.

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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 4 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: Answer each of the following as True or False justifying your answers:

a) [2 marks] If |A| = 1, then AX = O could have more than one solution.

b) [2 marks] Any square matrix A can be written as a sum of symmetric and skew-symmetric matrices.

c) [2 marks] If A is an n×n nonsingular matrix, then A5AT is also nonsingular matrix.

d) [2 marks] If A is an n×n nonsingular matrix such that A-1 = A, then A10 = In.

e) [2 marks] If X1, X2 and X3 are linearly dependent vectors in R3, then X3 is a linear combination of X1 and X2.

Q−2: Consider the linear system: .

a) [3 marks] Find |A|, A is the coefficient matrix for the linear system.

b) [2 marks] If possible, find the inverse of A.

c) [3 marks] Solve the linear system.

d) [2 marks] Change the third equation in the linear system to x y + z = 0. Is the new linear system consistent? Explain your answer.

Q−3: Let .

a) [6 marks] Find the matrix A.

b) [4 marks] Find |2A3ATA-1|.

Q−4: Let be a set of vectors in R3.

a) [4 marks] Determine whether the vectors in S are linearly independent.

b) [6 marks] Write, if possible, the vector as a linear combination of the vectors in S.

MT132 – Linear Algebra 2017-2018 / Second

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