5. Let x, y be vectors in R4, and let L be the set L = {ax +By: a, ß ER, 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, ß ER, 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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Correct solution.
![5. Let x, y be vectors in R4, and let L be the set
L = {ax +By: a, ß ER, 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3967d1ff-3154-4d39-960c-9b99329a7b21%2Fb4758056-3aa3-4c2b-8adf-d179964584e9%2Fcl39hwd_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let x, y be vectors in R4, and let L be the set
L = {ax +By: a, ß ER, 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).
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