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

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Roll No.

Total No. of Pages : 02

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Total No. of Questions : 07

B.Sc. (Computer Science) (2013 & Onwards) (Sem.-1)

ALGEBRA

Subject Code : BCS-101

M.Code : 70878

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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

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1. Write briefly :
   1. Define Transpose of the matrix.
   2. Define Orthogonal Matrix.
   3. Define Hermitian Matrix.
   4. Find the rank of the matrix :
   5. Find the inverse of the matrix :

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   6. Define Column Rank.
   7. Prove that the row rank of a matrix is the same as its rank.
   8. State conditions under which a set of homogenous equations possess a trivial solution?
   9. Define Nullity of a Matrix.
   10. 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.

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SECTION-B

2. Use Ferrari’s method to solve x⁴ — 8x² + 11x² + 20x + 4 = 0.
3. Use Cardan’s method to solve 2x³ — 7x² + 8x —3 = 0.

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4. Use Descartes’s method to solve x⁴— 2x² + 8x— 3 =0.
5. State and prove Cayley Hamilton theorem.
6. Find all the eigen values and vectors of the matrix
7. Find the minimal polynomial of the matrix

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.

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