Yahoo Answers: Answers and Comments for How to solve this linear algebra problem? [Mathematics]
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From Semi
enUS
Tue, 15 Feb 2011 13:18:57 +0000
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Yahoo Answers: Answers and Comments for How to solve this linear algebra problem? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20110215131857AAF8AKf
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From Astral Walker: So there must be some c1, c2, c3 such that
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https://answers.yahoo.com/question/index?qid=20110215131857AAF8AKf
https://answers.yahoo.com/question/index?qid=20110215131857AAF8AKf
Tue, 15 Feb 2011 21:30:34 +0000
So there must be some c1, c2, c3 such that
c1*f + c2*g + c3*h = p
c1(1 + 2t^2) + c2(1 + t) + c3(1 + 2t + t^2) = 3 + 9t^2
Now collect all terms.
(c1 + c2 + c3) + (c2 + 2c3)t + (2c1 + c3)t^2 = 3 + 9t^2
So now you have 3 equations and 3 unknowns. You can solve this via matrices but this seems straightforward to solve via substitution.
Matching all the coefficients you get
c1 + c2 + c3 = 3
c2 + 2c3 = 0 > c2 = 2c3
2c1 + c3 = 9 > c1 = (9  c3)/2
Substituing you get
(9  c3)/2  2c3 + c3 = 3
4.5  3c3/2 = 3
9  3c3 = 6
c3 = 1
c2 = 2
c1 = 4
So now go back to the original equation and substitue the coefficients.
4f(t)  2g(t) + h(t) = p(t)