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3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
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1-Determine if W is a subspace of Mnn CEMnn, W = {AEMnn: CA'C²= A} 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x2,1 + x + 4x²,1 – 7x 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?
Transcribed Image Text:1-Determine if W is a subspace of Mnn CEMnn, W = {AEMnn: CA'C²= A} 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x2,1 + x + 4x²,1 – 7x 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?
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