2) Let X be a finite dimensional vector space and S, T are subsets of X such that SST then a) If S basis for X then T basis for X. b) If T generate X then S generate X. c) If T basis for X then S basis for X. d) If S generate X then T generate X. 3) Let Z, be ring integers mode 5 and f(x) € Z5 (x) such that f(x) = x² + 2x + 1 then a) f(x) has only one root. b) f(x) has only two roots. c) f(x) irreducible polynomials. d) No one of above. 4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and multiplication of matrices then: a) F is a commutative ring but not field. b) F is a division ring and not field. c) If F an integral domain and F is not field. d) No one of above.

2) Let X be a finite dimensional vector space and S, T are subsets of X such that SST then a) If S basis for X then T basis for X. b) If T generate X then S generate X. c) If T basis for X then S basis for X. d) If S generate X then T generate X. 3) Let Z, be ring integers mode 5 and f(x) € Z5 (x) such that f(x) = x² + 2x + 1 then a) f(x) has only one root. b) f(x) has only two roots. c) f(x) irreducible polynomials. d) No one of above. 4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and multiplication of matrices then: a) F is a commutative ring but not field. b) F is a division ring and not field. c) If F an integral domain and F is not field. d) No one of above.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...

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