University of Sargodha BSIT 3d Term Exam 2015 Subject: BSIT. Course: Linear Algebra Paper:MATH-3215 Maximum Marks: 80

University of Sargodha

BSIT 3d Term Exam 2015

Subject: BSIT. Course: Linear Algebra Paper: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)

1.

Find the angle between u and v, u = (1,-5,1) ; v = (0,0,-1).

What is characteristic equation?

ill.

Define Eigen Vector

iv.

What are different types of distributions?

V.

Define similar matrices.

vi.

What are dependent vectors, give example.

vii.

What is meant by reduced echelon form of matrix?

vill.

Give example of augmented matrix.

ix.

ustad prove (AB)" = B'A

What are similar matrices?

Under what condition U and V vectors said to be orthogonal

xii.

What are linear independent vectors?

xili.

Define Basis of a matrix? U

xiv.

What is mean by subspace?

XV.

Find A", A= |10

XVI.

Solve the matrix equation for a,b, and : 13a c 22-a-16

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Subjective Part

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

Q.2. solve the linear system of equation by Guass- Jordan elimination.

x_ + 2x2 - 3x3=6

• 2x1-x2+ 4x3 = 1

Xy - X2 + X3

= 3

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 + 5z =2

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

Q.4. Find Eigen values and Eigen vectors all the minors and cofactors of given matrix

-2

3

ustads.

Find the rank and nullity of the matrix

-2

4

A=

- 1

5

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4

Q.6. Find LU- decomposition of A =

4

6

-10

Q.7 Find A, A =

-10

8.

2

01

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