1. Given, the vectors --(;) --()} u2 = = In (a) Determine if these vectors lie in the linear envelope Span {v1, v2} of the vectors () (:) V2 = v1 = If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors ul and u2 as linear combinations of v1 and v2 in more ways than one. (c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.

1. Given, the vectors --(;) --()} u2 = = In (a) Determine if these vectors lie in the linear envelope Span {v1, v2} of the vectors () (:) V2 = v1 = If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors ul and u2 as linear combinations of v1 and v2 in more ways than one. (c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 22EQ

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