et V = P2(R), give V the inner product defined by (f,9) = So 5(t)g(t) dt, and let W = span {1 – x}. (a) Explain why w+ = {a+ bx+ cr² : [ (1– z)(a + bx + cz²) dx = 아.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Hello, I need help with this Linear Algebra exercise, please. Thank you!

Let V = P2(R), give V the inner product defined by (f,g) = So f(t)g(t) dt, and let W = span {1 – 1}.
(a) Explain why Wt = br + cz² : So(1 – x)(a + bx + cr²) dx = 0} .
{a +
(b) Calculate ſ (1 – #)(a + bx + cx²) d.r, and use the direct result of this calculation together with the result
of part (a) to find a basis for W+. Show your work, and also make sure to prove that your answer really
is a basis for w+.
Transcribed Image Text:Let V = P2(R), give V the inner product defined by (f,g) = So f(t)g(t) dt, and let W = span {1 – 1}. (a) Explain why Wt = br + cz² : So(1 – x)(a + bx + cr²) dx = 0} . {a + (b) Calculate ſ (1 – #)(a + bx + cx²) d.r, and use the direct result of this calculation together with the result of part (a) to find a basis for W+. Show your work, and also make sure to prove that your answer really is a basis for w+.
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