1. Consider x +y+ z+ 2w + v 3x + 4y + 3z + 3w + 5v W = — 2я — Зу — w - 6у |x, y, z, w E R 2ж + 4у + 22—— 2w + 6v 3x + 2y + 3z + 9w + v which is a subspace of V = R° (DO NOT SHOW THIS ANYMORE).
1. Consider x +y+ z+ 2w + v 3x + 4y + 3z + 3w + 5v W = — 2я — Зу — w - 6у |x, y, z, w E R 2ж + 4у + 22—— 2w + 6v 3x + 2y + 3z + 9w + v which is a subspace of V = R° (DO NOT SHOW THIS ANYMORE).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
i. Find a spanning set for W
ii. Trim that spanning set in (i) to form a basis of W. Describe dim W.
iii. Extend that basis in (ii) to a basis of V.
iv. Based on your answer in (iii), find a subspace W' of V such that W⊕ W' = V.
![1. Consider
x +y+ z+ 2w + v
3x + 4y + 3z + 3w + 5v
W =
— 2я — Зу — w - 6у
|x, y, z, w E R
2ж + 4у + 22—— 2w + 6v
3x + 2y + 3z + 9w + v
which is a subspace of V = R° (DO NOT SHOW THIS
ANYMORE).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6ca3ee5-1b38-476e-aa72-cc7752f8cc61%2F27b1b28c-4cb2-4b9e-ab87-0b81c897a043%2Fm3bfx8a_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider
x +y+ z+ 2w + v
3x + 4y + 3z + 3w + 5v
W =
— 2я — Зу — w - 6у
|x, y, z, w E R
2ж + 4у + 22—— 2w + 6v
3x + 2y + 3z + 9w + v
which is a subspace of V = R° (DO NOT SHOW THIS
ANYMORE).
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