Basis is a set but not a matrix
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!
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.