For the given lists L and vector spaces V, use basic dimension arguments to say what you | can about L. Is it linearly independent? Does L span V? (If there is no nice dimension argument, just write "requires computation" for full credit.) (a) L {1,2x3,3 - a2} and V p3(R) 1,2 x, - a2,4 - x 3} and V = p3(R). (b) L (c) L {1,2 x x3,3- 2,4 - x + x3, 2+x} and V = p3(R) 1,2 x3,-x2,4 -x+x3,2+ x} and V = span (1 - x, 3x x2, 3x - 3) |(d) L

For the given lists L and vector spaces V, use basic dimension arguments to say what you | can about L. Is it linearly independent? Does L span V? (If there is no nice dimension argument, just write "requires computation" for full credit.) (a) L {1,2x3,3 - a2} and V p3(R) 1,2 x, - a2,4 - x 3} and V = p3(R). (b) L (c) L {1,2 x x3,3- 2,4 - x + x3, 2+x} and V = p3(R) 1,2 x3,-x2,4 -x+x3,2+ x} and V = span (1 - x, 3x x2, 3x - 3) |(d) L

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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