الان حل واجب
MT132: Linear Algebra
Tutor Marked Assignment
Cut-Off Date: December --, 2021 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:
If A is a 5×5 skew symmetric matrix such that 5A+BT-3I5=5(B-A)T, then B=345.
If A=1 -1 0 2 , B=1 2 and C is a 2×1 matrix such that A-1C=B and AC=D, then D=-5 8 .
If B and C are both inverses of the matrix A, then B=C.
If 1 3 x-5 1 0 0 2 x 1 =x 1 -2 x , then x=-1.
If X and Y are linearly independent vectors in Rn, then {O,X,Y} is linearly independent.
Q−2: [6+4 marks]
Let A=1 2 3 -1 0 2 3 -2 1 , B=1 2 1 2 2 3 1 3 -1 and C=1 0 1 2 1 1 1 1 -1 . If possible, compute (AT-B)T+C(B-1C)-1 and BTA.
Solve the linear system: { 3x2-6x3+6x4 +4x5=-5 3x1-7x2+8x3-5x4+8x5=9 3x1-9x2+12x3-9 x4+6x5=15 2x2-4x3+4x4 +2x5=-6 .
Q−3: [6+4 marks]
Let A=1 0 2 2 0 a 0 2 -a . Find all values of a for which the matrix A has inverse. Find A-1 (in terms of a) for the cases where it exists.
Let A=2 1 2 3 6 2 4 8 1 -1 0 4 0 1 -3 -4 . By transforming A to upper triangular form find A.
Q−4: [5+5 marks]
Find the value(s) of c for which the following vectors v1=1 0 0 1 , v2=0 1 -1 1 , v3=-1 0 -1 0 and v4=1 1 1 c are linearly independent.
Express the vector (-1,5,-6) in R3as a linear combination of (2,0,7), (2,4,5) and (2,-12,13)