Download PTU B.Sc CS-IT 2020 March 6th Sem 72782 Linear Algebra Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B-Sc CSE-IT (Bachelor of Science in Computer Science) 2020 March 6th Sem 72782 Linear Algebra Previous Question Paper

1 | M-72782 (S3)-2136

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc.(CS) (2013 & Onwards) (Sem.?6)
LINEAR ALGEBRA
Subject Code : BCS-602
M.Code : 72782
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
Q1 Answer the followings in short :
a) Define Groups.
b) Define Field.
c) Define Vector Spaces.
d) Define Linear dependent.
e) Define Quotient Space.
f) Define Linear Transformations.
g) If T is a linear operator on V such that T
2
? T + I = 0. Prove that T is invertible.
h) Define isomorphism.
i) Define Nullity of a Matrix.
j) If V and W are finite dimensional vector spaces such that dimV = dimW. Then prove
that a linear transformation T : V ? W is one-one iff T is onto.

FirstRanker.com - FirstRanker's Choice
1 | M-72782 (S3)-2136

Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc.(CS) (2013 & Onwards) (Sem.?6)
LINEAR ALGEBRA
Subject Code : BCS-602
M.Code : 72782
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.

SECTION-A
Q1 Answer the followings in short :
a) Define Groups.
b) Define Field.
c) Define Vector Spaces.
d) Define Linear dependent.
e) Define Quotient Space.
f) Define Linear Transformations.
g) If T is a linear operator on V such that T
2
? T + I = 0. Prove that T is invertible.
h) Define isomorphism.
i) Define Nullity of a Matrix.
j) If V and W are finite dimensional vector spaces such that dimV = dimW. Then prove
that a linear transformation T : V ? W is one-one iff T is onto.

2 | M-72782 (S3)-2136

SECTION-B
Q2 Prove that the union of two subspaces is a subspace if and only if one of them is
contained in other.
Q3 Write the vector v = (1, ?3,5) belongs to the linear space generated by S, where
S = {(1,2,1), (1,1,-1), (4,5, -2)} or not?
Q4 State and prove Existence theorem for basis.
Q5 State and prove Rank-Nullity theorem.
Q6 Let T be a linear operator on R
2
defined by T(x,y) = (4x ? 2y, 2x + y) Find the matrix of T
relative to the basis B = {(1,1); (?1,0)}.
Q7 Prove that the characteristic and minimal polynomials of an operator or a matrix have the
same roots except for multiplicities.











NOTE : Disclosure of identity by writing mobile number or making passing request on any
page of Answer sheet will lead to UMC case against the Student.

FirstRanker.com - FirstRanker's Choice