Linear Algebra help please
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Linear Algebra help please

[From: ] [author: ] [Date: 11-08-09] [Hit: ]
yahoo.We found that given a + bx + cx^2 + dx^3 in P3,a + bx + cx^2 + dx^3 = C₁*1 + C₂(1 - x) + C₃(2 - 4x + x^2) + C₄(6 - 18x + 9x^2 - x^3),C₁ = a + b + 2c + 6d, C₂ = -b - 4c - 18d, C₃ = c + 9d,......
Let B={1, 1-x, 2-4x+x^2, 6-18x+9x^2-x^3} and p(x)=7-8x+3x^2
Find [p(x)]B
Please leave as many details as you can so I can fully understand. Thanks so much for the help!

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From your previous post:
http://answers.yahoo.com/question/index;…

We found that given a + bx + cx^2 + dx^3 in P3, we have
a + bx + cx^2 + dx^3 = C₁*1 + C₂(1 - x) + C₃(2 - 4x + x^2) + C₄(6 - 18x + 9x^2 - x^3), where
C₁ = a + b + 2c + 6d, C₂ = -b - 4c - 18d, C₃ = c + 9d, and C₄ = -d.

For p(x) = 7 - 8x + 3x^2, note that a = 7, b = -8, c = 3, d = 0.
So, C₁ = 5, C₂ = -4, C₃ = 3, and C₄ = 0.

Hence, [p(x)]B = (5, -4, 3, 0), the vector of coefficients from the vectors in B.

I hope this helps!
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