University of Sargodha BS 4* Term Examination 2015 Subject: Computer Science Paper: Linear Algebra (Math-3215) Maximum Marks: 80

University of Sargodha

BS 4* Term Examination 2015

Subject: Computer Science Paper: Linear Algebra (Math-3215)

Maximum Marks: 80

Time Allowed: 2:30 Hours

Objective Part Compulsory

Q.No1. Write short answers of the following questions. (16*2-32)

i.

Find all values of coz and ca ; c, (-1,0,2) + c.(2,2,-2) + c(1,-2,1) = (-6,12,4)

il./Find u.v; u = (2,1,-2,4), v = (0,-1,-3,1)

Hi.

Which of the following are sub-spaces of R'

All vectors of the form (a,0,0)

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All vectors of the form (a, 1,0)

Find the standard matrix for the transformation defined by the formula

(*_ X2, xg) = (x,+2x,+Xg, x;+5x2, x3)

Define Eigen values.

vii.

vili.

state Cauchy-Schwarz inequartstadni.co

Define inner product.

if u = (5, -1,

2) then find norm of u.

ix.

What are orthonormal basis, provide example

x. Prove (AB)" = B'A'

xi.

if u = (5, -1, 2), find norm of u.

xii.

Define symmetric matrix

xil.

Define a diagonal matrix with example.

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xiv

Check whether A is singular or not? A =

XV.

XVI.

What is characteristic equation?

Define similar matrices.

Subjective Part

Attempt any four out of six questions (4*12-48)

0.2. Do the polynomials t +2t+1, f-t+2, 1'+2, +'+*-5t+2 span P*

Q.3. Determine the values of 'a' for which the system has non- solution, exactly one solution and

infinitely many solution.

x + 2y - 3z = 4

3x-y + 52 =2

4x + y + (a'-2) z = a+4

Q.4. Find Eigen values and Eigen vectors for following matrix/

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-2

com

0.5. Solve the linear system by Gauss-jordan (Row reduced Echelon form) elimination "

- 2x2 + 3X3

= 1

3x, +6x2 + 3xз = -2

6xy - 6x2 + 3xg = 5

= 4*

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0.6. If A =

-21

4 then verify that det(A) = det(A')

-3

Q.7. Compute adjoint of A and A1

- 2

A =

-31

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