Firstranker's choice
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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 :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- 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 :
- Define Groups.
- Define Field.
- Define Vector Spaces.
- Define Linear dependent.
- Define Quotient Space.
- Define Linear Transformations.
- If T is a linear operator on V such that T2 — T+ I = 0. Prove that T is invertible.
- Define isomorphism.
- Define Nullity of a Matrix.
- 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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Firstranker's choice
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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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This download link is referred from the post: PTU B-Sc CS-IT 2020 March Previous Question Papers