Question

Find the coordinate vector x+x^4 in P4 relative to the basis (1, 2x-1, x^3+x^4, 2x^3,x^2+2)?

Answer 1

Here is what I think to do: create matrix
1 -1 0 0 2
0 2 0 0 0
0 0 0 0 1
0 0 1 2 0
0 0 1 0 0

Answer 2

add new vector to other matrix and reduce.

Answer 3

or multiply by new vector to create a change of basis

Answer 4

i believe the basis of the system stated is:

x^: 0 1 2 3 4
---------------
1 0 0 0 0
-1 2 0 0 0
0 0 0 1 1
0 0 0 2 0
2 0 1 0 0

Answer 5

AX = B

the coordinant vector X relative to the basis A, is B

let X = [0 1 0 0 1]

Answer 6

... or do i have that backwards

Answer 7

ok, X is the coordinant vector

\[[X]_A:~AB = X\]

does that sound familiar?