University of Sargodha BS 4® Term Examination 2017. Subject: Computer Science Paper: Linear Alpebra (MATH:3215) Maximum Marks: 80

University of Sargodha

BS 4® Term Examination 2017.

Subject: Computer Science Paper: Linear Alpebra (MATH:3215)

Maximum Marks: 80

Time Allowed: 2:30 Hours

Note: Objective part is compulsory. Attempt any three questions from subjective part.

Objective Part

(Compulsory)

Q. No. 1 Write short answers of the following in 2-3 lines cach.

Define the subspace of a vector space?

(11)

(111)

What do you mean by Eigen vector and Eigen values?

Define the Fourier series?

What do you mean by the diagonal matrix?

Define basis of a vector space?

Define lincar equation by writing its standard form?

What do mean by the positive definite matrices?

Define a characteristic equation?

Jeline symmetric matrix by giving an example?

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Write the standard basis for R°?

(xiD)

Define linear equation in xy-plane?

(xiii)

(xIN)

Jefine linearly independent veegers By giving an example

Define dimension of vectot spate and subspace

(xy)

(xvi)

(2*16)

1-1 2+1

Subjective Part

(3*16)

Q. No. 2: Find the characteristic equation, Eigen values and the corresponding Eigen vectors for the

given matrix

02 e 5 da: so te paropeis r nie daremian.

Q. No. 3

(a): Solve for x:

2+ x

3

3+ x

det

2

= 0

(b): Write the vector v-(23 2X

as a lincar combination of vi-(1,1,1).

Q. No. 4

(a): Find the rank of the matrix

2

15

8

111

112

5

8

8

7

10

(b): Find the inverse of the given matrix by cofactor method.

N

-1

2- (1,2,3), v. - (2,-1,1).

0

2

Q. Nor6: Find the solution of the following system of linear equations by using Gauss-Jordan method;

2x]-X2-X3

-4.

3x1+4x2-2x,=11.

3x1-2x2+4x,-11.

12

A =

2

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