MT132 : Linear Algebra
Tutor Marked Assignment
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 6
Q_2 8
Q_3 8
Q_4 8
30
General Comments:
Tutor name:
The TMA covers only chapters 1 and 2. It consists of four questions; you should give the details of your solutions and not just the final results.
Q−1: [3×2 marks] Answer each of the following as True or False justifying your answers:
If A=[■(1&2@0&t)] and A^2-I_2= O, then t=-1.
If A=[■(1&1&2@2&1&1@3&3&3)], then there exists a 3×3 matrix B such that AB=I_3.
The vector X=(1,1,1) in R^3 is a linear combination of the vectors X_1=(0,1,-1) and X_2=(1,-1,2).
Q−2: [4+4 marks]
Find all values of a for which the linear system {■(x+2y+az=1@x+3y+(1-a)z=3@x+4y+(1+2a)z=5)┤
Has:
No solution;
a unique solution or
has infinitely many solutions.
Solve the linear system {■(x+y+z=2@x+2y+z=5@y=3)┤.
Q¬−3: [4+4 marks]
Let A=[■(-1&0&1@-3&1&1@2&0&-1)] and B=[■(1&2&3@2&4&-1@3&-1&5)].
Find, if it exists, A^(-1).
Find a matrix C such that (AC+B)^T=A^T+B.
Let A=[■(1&2@3&4)],B=[■(1@2)] and A^(-1) C=B. Find a matrix X such that X=AC.
Q−4: [4+4 marks]
Let S={[■(1@2@3)],[■(0@1@2)],[■(-1@0@2)]} be a set of vectors in R^3 and X=[■(-2@4@13)] be a vector in R^3. If possible, write X as a linear combination of vectors in S.
Let S={X_1,X_2,X_3} be a linearly independent set of vectors inR^3. Determine whether T={2X_1+X_2-2X_3,4X_1+3X_2 ,3X_1+2X_2- X_3} is linearly independent.