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- Let S be a subset of a vector space V over a field F, then a) if S is linearly independent then S generates V. b) if S generates V then S is linearly independent. c) if S is linearly independent then S in a basis for V. d) if S is a basis for V then S is linearly independent.

- Let S be a subset of a vector space V over a field F, then a) if S is linearly independent then S generates V. b) if S generates V then S is linearly independent. c) if S is linearly independent then S in a basis for V. d) if S is a basis for V then S is linearly independent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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- Let S be a subset of a vector space V over a field F, then a) if S is linearly independent then S generates V. b) if S generates V then S is linearly independent. c) if S is linearly independent then S in a basis for V. d) if S is a basis for V then S is linearly independent. Let M, be a ring of 2×2 matrices under usual addition and multiplication thea a) M; is a commutative ring with unity. b) M; is a division ring. c) M; is a ring with unity. d) M; is an integral domain.
Transcribed Image Text:- Let S be a subset of a vector space V over a field F, then a) if S is linearly independent then S generates V. b) if S generates V then S is linearly independent. c) if S is linearly independent then S in a basis for V. d) if S is a basis for V then S is linearly independent. Let M, be a ring of 2×2 matrices under usual addition and multiplication thea a) M; is a commutative ring with unity. b) M; is a division ring. c) M; is a ring with unity. d) M; is an integral domain.
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