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W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space, say W = {w₁, w₁, W3, w}} that have the following property: 1. Applying the plus/minus theorem, you can pick two vectors from W, say W' = {wi, w2} so that span(W') = span(W). Prove, using the minus part of the plus/minus theorem that your vectors meet the above conditions. Then, explain in words how you created your set of vectors so that this worked out.

W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space, say W = {w₁, w₁, W3, w}} that have the following property: 1. Applying the plus/minus theorem, you can pick two vectors from W, say W' = {wi, w2} so that span(W') = span(W). Prove, using the minus part of the plus/minus theorem that your vectors meet the above conditions. Then, explain in words how you created your set of vectors so that this worked out.

Advanced Engineering Mathematics
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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Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space, say W = {w}, w½, w3, w4} that have the following property: {w, w} 2} so that span(W') = span(W). 1. Applying the plus/minus theorem, you can pick two vectors from W, say W' = {w Prove, using the minus part of the plus/minus theorem that your vectors meet the above conditions. Then, explain in words how you created your set of vectors so that this worked out.
Transcribed Image Text:Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space, say W = {w}, w½, w3, w4} that have the following property: {w, w} 2} so that span(W') = span(W). 1. Applying the plus/minus theorem, you can pick two vectors from W, say W' = {w Prove, using the minus part of the plus/minus theorem that your vectors meet the above conditions. Then, explain in words how you created your set of vectors so that this worked out.
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