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2. Let W be an (n – 1)-dimensional subspace of V. Show that V has a basis B satisfying Bn W = Ø.

2. Let W be an (n – 1)-dimensional subspace of V. Show that V has a basis B satisfying Bn W = Ø.

Linear Algebra: A Modern Introduction
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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Please do part 2!

1. Let (e1, ... , en) be a basis for a vector space V. Show that (e1 + en, e2 + en, en-1 + en, en) is also a ... , basis for V. 2. Let W be an (n – 1)-dimensional subspace of V. Show that V has a basis B satisfying BnW = Ø.
Transcribed Image Text:1. Let (e1, ... , en) be a basis for a vector space V. Show that (e1 + en, e2 + en, en-1 + en, en) is also a ... , basis for V. 2. Let W be an (n – 1)-dimensional subspace of V. Show that V has a basis B satisfying BnW = Ø.
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