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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