For P2(R)is the vector space of polynomials of degree at most 2.
a standard basis, B is given by $(1,x,x^2)$
C is also a basis given by $(x^2-x, x, -x^2+x+1)$
How do i find the change of matrix [C]B and then find [B]C ? It would really mean a lot if I can get a solution to this.
To find the matrix $[C]_B$ , Take each polynomial from C and make this equation : for example : (definition of c is scalars)
$x^2-x=c_1*1+c_2*x+c_3*x^2$ (after you solve this , take the scalars and put them in a matrix a the first column)
$x=c_1*1+c_2*x+c_3*x^2$
$-x^2+x+1=c_1*1+c_2*x+c_3*x^2$
after you solve the three equations and put them in a matrix , this is the transformation matrix.
Do the same with the other basis but now (or find the inverse of the matrix) $\Rightarrow$ The left side of the equation will be a vector from the basis $B$ and the right side of the equation will be scalars multiplied by the vectors of the basis $C$.