- #1
cscott0001
- 6
- 1
Homework Statement
Find the coordinates of each member of set S relative to B.
B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)}
S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)}
I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate points to create a 6x6 system that solves for the coordinates of each element of S.
Homework Equations
Ax = b
If I was given a simpler problem, such as "Find the coordinate vector of w = (1, 0) relative to the basis S = {u, v}, u = (2, 2) and v = (1, 1)" my equation would start:
(1, 0) = k1(2, 2) + k2(1, 1)
and I'd solve for k1 and k2
The Attempt at a Solution
I started with the equation S = kB, where k is a constant, but I was told to build a 6x6 matrix by sampling each member of B at six points, so I knew that's wasn't right. I built a 6x6 matrix from B with columns 1-6 filled with evaluations of B with x = {0, pi/6, pi/4, pi/3, pi/2, pi}, but I don't think that's right either, because I didn't create any spanning equations. I tried using a matrix {{1,0,0,0,,00},{0,cos(x),0,0,0,0}...{0,0,0,0,0,cos5(x)}}, to test for span, but that didn't feel right either. How do I create spanning equations to sample to build the matrix?