5. Let x, y be vectors in R4, and let L be the set L = {ax +By: a, BER, a + B = 1}. (a) Verify that L is an affine subspace of R4 (i.e., if w₁, W2 are in L then so is any affine combina- tion). (b) Suppose x = [1 2 3 4]" and y = [0 1 2 3]¹. Find a vector u and a matrix A such that L = u + null(A).

5. Let x, y be vectors in R4, and let L be the set L = {ax +By: a, BER, a + B = 1}. (a) Verify that L is an affine subspace of R4 (i.e., if w₁, W2 are in L then so is any affine combina- tion). (b) Suppose x = [1 2 3 4]" and y = [0 1 2 3]¹. Find a vector u and a matrix A such that L = u + null(A).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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