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Show your work / explain your reasoning! 1. Let W = Span{(2, –3,0, 1), (4, –6, –2, 1), (6, –9, –2, 2)}C 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, WW+ and the rank and nullity theorem.

Show your work / explain your reasoning! 1. Let W = Span{(2, –3,0, 1), (4, –6, –2, 1), (6, –9, –2, 2)}C 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, WW+ and the rank and nullity theorem.

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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please answer d, e parts
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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