Let a, b ∈ R. a) Find the determinant of a 2 b -2 1 2 4 -2 -1 b) Suppose u, v, and w are linearly independent vectors in a vector space V . Use your answer to (a) to find the values of a and b such that the vectors: au − 2v + 4w, 2u + v − 2w, and bu + 2v − w are linearly dependent. (use part a)

Let a, b ∈ R. a) Find the determinant of a 2 b -2 1 2 4 -2 -1 b) Suppose u, v, and w are linearly independent vectors in a vector space V . Use your answer to (a) to find the values of a and b such that the vectors: au − 2v + 4w, 2u + v − 2w, and bu + 2v − w are linearly dependent. (use part a)

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 16EQ

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