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7.) Find a basis for the subspace V of R4 consisting of all vectors of the form (a, b, c, a +b+c), and state its dimension. Another way or writing this subspace is V = {(a, b, c, d) : d = a +b+c}

7.) Find a basis for the subspace V of R4 consisting of all vectors of the form (a, b, c, a +b+c), and state its dimension. Another way or writing this subspace is V = {(a, b, c, d) : d = a +b+c}

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
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Based on other problems I believe the dimension is 3, but I'm not sure how to find a basis given this subspace.

7.) Find a basis for the subspace V of R4 consisting of all vectors of the form (a, b, c, a + b + c), and state its dimension. Another way or writing this subspace is V = {(a, b, c, d) : d=a+b+c}
Transcribed Image Text:7.) Find a basis for the subspace V of R4 consisting of all vectors of the form (a, b, c, a + b + c), and state its dimension. Another way or writing this subspace is V = {(a, b, c, d) : d=a+b+c}
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