MT132 (M132): Linear Algebra Tutor Marked Assignment Cut-Off Date: ---, 2018 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..……………………… 3 Q

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MT132 (M132): Linear Algebra Tutor Marked Assignment Cut-Off Date: ---, 2018 Total Marks: 40 Contents Feedback form ……….……………..…………..…………………….…...….. 2 Question 1 ……………………..………………………………………..……… 3 Question 2 ……………………………..………………..……………………… 3 Q

مُساهمة  whatsapp::00966542495275 في الأربعاء مارس 14, 2018 9:42 pm







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
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Student Name :_____________________
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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:

[2 marks] If |A| = 1, then AX = O could have more than one solution.
[2 marks] Any squarematrixA can be written as a sum of symmetric and skew-symmetric matrices.
[2 marks] If A is an n×nnonsingular matrix, then A5AT is also nonsingular matrix.
[2 marks] IfA is an n×nnonsingular matrix such that A-1 = A, then A10 = In.
[2 marks] If X1, X2 and X3 are linearly dependent vectors in R3, then X3 is a linear combination of X1andX2.










Q−2: Consider the linear system: {■(x+2z=1@2x+y+5=2@x-y+z=1)┤.
[3 marks] Find |A|, A is the coefficient matrix for the linear system.
[2 marks] If possible, find the inverse ofA.
[3 marks] Solve the linear system.
[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^(-1)=[■(1&2&-2&1@1&2&-1&0@2&5&-6&4@-2&-4&4&-1)].
[6 marks]Find the matrix A.
[4 marks]Find |2A3ATA-1|.














Q−4:Let S={[■(-1@2@1)],[■(1@0@1)],[■(1@1@1)] } be a set of vectors in R3.
[4 marks]Determine whether the vectors inS are linearly independent.
[6 marks] Write, if possible, the vector [■(-4@4@-6)] as a linear combination of the vectors in S.

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