Let V be a 2-dimensional inner product space, and suppose that e', e2 is an orthonormal basis for V. Suppose that v1, v2 E V are such that 1 and ||v2 – e2|| < V2 1 ||v1 – e|| < V2 Show that v, v2 forms a basis for V.

Let V be a 2-dimensional inner product space, and suppose that e', e2 is an orthonormal basis for V. Suppose that v1, v2 E V are such that 1 and ||v2 – e2|| < V2 1 ||v1 – e|| < V2 Show that v, v2 forms a basis for V.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 22EQ

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Question

Let V be a 2-dimensional inner product space, and suppose that e', e²
is an orthonormal basis for V. Suppose that v1, v2 E V are such that
1
and ||v2 – e2|| <
V2
1
|lv1 – e1|| <
V2
Show that v1, v2 forms a basis for V.

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