Consider the following vectors in R³: V1 = W1 = V2 = W2 = W3 = -14] Let V be the subspace spanned by {w1, W2, ‚W3}. Find a linearly independent set of vectors {V₁, V₂} that spans V, so that neither v₁ nor v₂ is a scalar multiple of any of w₁, W2, W3. 19

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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Consider the following vectors in R³:
V1 =
W₁ =
V2 =
5
2
W2 =
2
-5
2
W3 =
Let V be the subspace spanned by {w₁, W2, W3}.
Find a linearly independent set of vectors {v₁, v₂} that spans V, so that neither v₁ nor v₂ is a scalar multiple of any of W1, W2, W3.
19
Transcribed Image Text:Consider the following vectors in R³: V1 = W₁ = V2 = 5 2 W2 = 2 -5 2 W3 = Let V be the subspace spanned by {w₁, W2, W3}. Find a linearly independent set of vectors {v₁, v₂} that spans V, so that neither v₁ nor v₂ is a scalar multiple of any of W1, W2, W3. 19
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