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

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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

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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.

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SECTION-A

Q1 Answer the followings in short :

1. Define Groups.
2. Define Field.
3. Define Vector Spaces.

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4. Define Linear dependent.
5. Define Quotient Space.
6. Define Linear Transformations.
7. If T is a linear operator on V such that T² — T+ I = 0. Prove that T is invertible.
8. Define isomorphism.

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9. Define Nullity of a Matrix.
10. 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.

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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.

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Q6 Let T be a linear operator on R² 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.

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