1- 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 is a basis for V d) if S is a basis for V then S is linearly independent. 2- Let M₂ be a ring of 2×2 matrices under usual addition and multiplication then a) M2 is a commutative ring with unity. b) M2 is a division ring. c) M2 is a ring with unity. d) M2 is an integral domain. 3- Let Σan and Σb, are two infinite series such that 0 ≤an ≤b, then a) if a converges then Σb, converges. b) if Σb, diverges then Σa, diverges. c) if Σb converges then Σa, converges. d) if a converges then Σb, diverges. 4-Let (F+) be a field and ((3) be irreducible polynomial in F(x) then We f(x)> is a field. deal and need not to be a

1- 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 is a basis for V d) if S is a basis for V then S is linearly independent. 2- Let M₂ be a ring of 2×2 matrices under usual addition and multiplication then a) M2 is a commutative ring with unity. b) M2 is a division ring. c) M2 is a ring with unity. d) M2 is an integral domain. 3- Let Σan and Σb, are two infinite series such that 0 ≤an ≤b, then a) if a converges then Σb, converges. b) if Σb, diverges then Σa, diverges. c) if Σb converges then Σa, converges. d) if a converges then Σb, diverges. 4-Let (F+) be a field and ((3) be irreducible polynomial in F(x) then We f(x)> is a field. deal and need not to be a

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 7AEXP

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