# Math Help - coordinates given basis

1. ## coordinates given basis

I am stuck on this problem, i tried multiplying p(x) by B but the answer i got is incorrect, any help is appreciated

The set is a basis for . Find the coordinates of relative to this basis:

[p(x)]B=

2. Originally Posted by Juggalomike
I am stuck on this problem, i tried multiplying p(x) by B but the answer i got is incorrect, any help is appreciated

The set is a basis for . Find the coordinates of relative to this basis:

[p(x)]B=
You are looking for $c_1,c_2,c_3$ such that

$c_1(-1+4x^2)+c_2(-3+4x+12x^2)+c_3(-7+8x+36x^2)=-28+36x+144x^2$

Expanding this out gives

$(-c_1-3_2-7c_3)\cdot 1+(4c_2+8c_3)\cdot x+(4c_1+12c_2+36c_3)\cdot x^2=-28+36x+144x^2$

Now just solve the system of equations for the needed coeffients.

3. im confused, do you meen solve for c1 c2 and c3? or 1 x and x^2? Also, when solving for that coefficient do i set the others to 0?