حل واجب MT132 شرح واجب MT132 مدرس MT132 MT132 (M132): Linear Algebra Tutor Marked Assignment Cut-Off Date: August --, 2021 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………..…………………….…...….. 2 Question 1

حل واجب MT132
شرح واجب MT132
مدرس MT132
MT132 (M132): Linear Algebra
Tutor Marked Assignment
Cut-Off Date: August --, 2021 Total Marks: 40
Contents
Feedback form ……….……………..…………..…………………..…………………….…...….. 2
Question 1 ……………………..…………………………………..………………………..……… 3
Question 2 ……………………………..………………..…..……………………………………… 4
Question 3 ………………………………..…………………..………………..…………………… 5
Question 4 ………………..…………………………………..……………………..……………… 6
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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 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=-1 3 -3 1 with rATrA=5, then r=12 .
If A is a 3×3 matrix such that AX=O has only the trivial solution, then AX=1 2 3 has a unique solution.
If I2-2AT-1=2 1 1 1 , then A=0 12 12 -12 .
If A=1 -1 -1 3 and B=1 5 -1 0 , then 3A2AB-1T=725.
There exit values of a∈R such that the vectors 1,1,1,(2,2,2) and ,(3,a,4) are linearly independent.
Q−2: [4+6 marks]
Let A and B be two n×n matrices satisfying A+B-AT+BT=O. Show that A is a symmetric matrix and B is a skew symmetric matrix.
Consider the linear system: {x+3z+3w=1 y+z-w=0 x-2y+3z+w=0 2y+a2+1w=a+2 .
For which values of a does the linear system have
no solution;
a unique solution;
infinitely many solutions.
Q−3: [6+4 marks]
Let A=1 0 -1 -1 1 2 2 1 0 and B=2 1 2 -2 4 0 3 1 -1 . Find a 3×3 matrix C such that AC+B=I3.
Find all values of c∈R for which the matrix A=2 c c c c c 1 2 c is singular.
Q−4: [6+4 marks] Let A be a 3×3 matrix and let u=-1 8 -9 , v=1 2 -1 and w=2 -1 3 . Suppose Av=-v and Aw=2w.
Find the vector Au.
Find the vector A5u.