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Linear Algebra MS Computer Science/MSc Computer Science/PhD Computer Science 2 Semester/Term PU — University of the Punjab 2023

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Ayesha Mustafa· 1 day ago

BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025

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Abubakar· 1 day ago

Literary criticism

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Guest· 2 days ago

this paper consists of 60 marks but now we have 35 marks paper.

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Annie· 2 days ago

Can you please tell me more past papers please because my exams are starting from next week

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Ahmed· 6 days ago

Did you provide the past papers of the science of society uos?

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Paper text

UNIVERSITY OF THE PUNJAB

B.S. in Computer Science / Second Semester - Spring 2023

Subject: Linear Algebra

Paper: MS-153

Roll No.

「キキキキキす•、

Time: 3 Hrs. Marks: 60

THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDED

Solve the followings:

(6x5=30)

Show that the matrix

-10

is an involutary matrix.

0 1

0.4

Q.S

Q,6

Evaluate

Prove that < u, >= 11 - 21⅓ - 2421 + 54g is an inner product on Ri

Where 1 = （L,1.），Dー（U1.5）ER.

Determine whether the set of rational numbers Q is a subspace of the vector space R.

Check whether the transformation T: R? → Ra defined by

T(x,*2, xx) = (x) - X2, *2 - Xg,,) is linear or nonlinear.

Show that AAFis symmetric for any square matrix A.

Solve the followings.

(5x6=30)

Use Gauss-Jordan method to solve the following system of equations.

5x1-2x,+xy = 2

3x1+2x+7x=3

十五＋3x=2

8 by adjoint method.

Determine whether or not the vectors (5,3, -3), (1,0,0) and (0,1, -1) are linearly

11 5

51287

101

Fload the irve of the marte A -

independent or linearly dependent.

Q10

Find the rank of the matrix

Q.11

Find the eigenvalues and eigenvectors of the matrix