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6. Let V = R³ and F = R. Let W = { (a, b, c) | a+b-2c=0 where a, b, c are in R} It can be shown that W is a subspace of V. (You do not have to check this.) (a) Find a basis for W and explain why it is a basis. (b) What is the dimension of W?

6. Let V = R³ and F = R. Let W = { (a, b, c) | a+b-2c=0 where a, b, c are in R} It can be shown that W is a subspace of V. (You do not have to check this.) (a) Find a basis for W and explain why it is a basis. (b) What is the dimension of W?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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6. Let V = R³ and F = R. Let W = { (a,b,c) | a+b=2c=0 where a, b, c are in R} It can be shown that W is a subspace of V. (You do not have to check this.) (a) Find a basis for W and explain why it is a basis. (b) What is the dimension of W?
Transcribed Image Text:6. Let V = R³ and F = R. Let W = { (a,b,c) | a+b=2c=0 where a, b, c are in R} It can be shown that W is a subspace of V. (You do not have to check this.) (a) Find a basis for W and explain why it is a basis. (b) What is the dimension of W?
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