Show your work / explain your reasoning! - 1. Let W = Span{(2, –3, 0, 1), (4, –6, –2, 1), (6, –9, –2, 2)} C Rª. (a) Find a basis for W. (b) Find a basis for W+. (c) Find an orthogonal basis for W and W-. (d) The union of these two orthogonal bases (put the basis for W and W- into one set) is an orthogonal basis for what? Why is the union orthogonal? (e) Explain the relationship between the dimension of W, W- and the rank and nullity theorem.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show your work / explain your reasoning!
1. Let
W %3 Spanf{(2, —3, 0, 1), (4, —6, —2, 1), (6, —9, —2, 2)} С R*.
(a) Find a basis for W.
(b) Find a basis for W-.
(c) Find an orthogonal basis for W and W.
(d) The union of these two orthogonal bases (put the basis for W and W- into one set) is
an orthogonal basis for what? Why is the union orthogonal?
(e) Explain the relationship between the dimension of W, w+ and the rank and nullity
theorem.
Transcribed Image Text:Show your work / explain your reasoning! 1. Let W %3 Spanf{(2, —3, 0, 1), (4, —6, —2, 1), (6, —9, —2, 2)} С R*. (a) Find a basis for W. (b) Find a basis for W-. (c) Find an orthogonal basis for W and W. (d) The union of these two orthogonal bases (put the basis for W and W- into one set) is an orthogonal basis for what? Why is the union orthogonal? (e) Explain the relationship between the dimension of W, w+ and the rank and nullity theorem.
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