Given the basis G =
1, -1/2, 1/4, -1/8
0, 1/2, -1/2, 3/8
0, 0, 1/4, -3/8
0, 0, 0, 1/8
And the polynomial v=
1 + x + x^2 + x^3
How can I find the coordinate vector (v)G ? I've only figured out that the answer should be a 4x1 column vector. Thanks for any help!
Basis is a set but not a matrix
Lol, why did I write that?
The basis G = (1, (2x+1), (2x+1)^2, (2x+1)^3)
Okay, then, you need to find numbers, a, b, c, and d, such that a(1)+ b(2x+1)+ c(2x+1)^2+ d(2x+1)^3= 1+ x+ x^2+ x^3 for all x. Multiply out the right side and set "corresponding coefficients" equal to get four equations for a, b, c, and d. Or, set x equal to any four numbers to get four equations.
Thanks! I'm still not able to set it up right... If I multiply out the parantheses I get
a + b2x + b + c4x^2 + c4x + c + d8x^3 + d12^x2 + d6x + d = 1 + x + x^2 + x^3
How to proceed?