Download PTU B.Sc CS-IT 2020 March 1st Sem 70878 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 1st Sem 70878 Algebra Previous Question Paper

1 | M - 7 0 8 7 8 ( S 3 ) - 1 8 7
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (Computer Science) (2013 & Onwards) (Sem.?1)
ALGEBRA
Subject Code : BCS-101
M.Code : 70878
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
1. Write briefly :
(a) Define Transpose of the matrix.
(b) Define Orthogonal Matrix.
(c) Define Hermitian Matrix.
(d) Find the rank of the matrix :
2 4
5 3
? ?
? ?
? ?

(e) Find the inverse of the matrix :
?1 5
4 ?3
? ?
? ?
? ?

(f) Define Column Rank.
(g) Prove that the row rank of a matrix is the same as its rank.
(h) State conditions under which a set of homogenous equations possess a trivial
solution?
(i) Define Nullity of a Matrix.
(j) If X be an eigen vector of the n-rowed square matrix A over a field F, then X cannot
correspond to two distinct eigen values.
FirstRanker.com - FirstRanker's Choice
1 | M - 7 0 8 7 8 ( S 3 ) - 1 8 7
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (Computer Science) (2013 & Onwards) (Sem.?1)
ALGEBRA
Subject Code : BCS-101
M.Code : 70878
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
1. Write briefly :
(a) Define Transpose of the matrix.
(b) Define Orthogonal Matrix.
(c) Define Hermitian Matrix.
(d) Find the rank of the matrix :
2 4
5 3
? ?
? ?
? ?

(e) Find the inverse of the matrix :
?1 5
4 ?3
? ?
? ?
? ?

(f) Define Column Rank.
(g) Prove that the row rank of a matrix is the same as its rank.
(h) State conditions under which a set of homogenous equations possess a trivial
solution?
(i) Define Nullity of a Matrix.
(j) If X be an eigen vector of the n-rowed square matrix A over a field F, then X cannot
correspond to two distinct eigen values.
2 | M - 7 0 8 7 8 ( S 3 ) - 1 8 7
SECTION-B
2. Use Ferrari?s method to solve x
4
? 8x
3
+ 11x
2
+ 20x + 4 = 0.
3. Use Cardan?s method to solve 2x
3
? 7x
2
+ 8x ? 3 = 0.
4. Use Descartes?s method to solve x
4
? 2x
2
+ 8x ? 3 = 0.
5. State and prove Cayley Hamilton theorem.
6. Find all the eigen values and vectors of the matrix
3 1 4
0 2 6
0 0 5
? ?
? ?
? ?
? ?
? ?

7. Find the minimal polynomial of the matrix
1 ?2 3
0 5 ?3
0 0 ?2
? ?
? ?
? ?
? ?
? ?










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