Hi I was wondering if anyone could help me with part d) e) and f) of this linear algebra question.
So far I have found:
a) $T(x^2 - 2x + 1)= 3x^2 - 5x - 1$ using linear map definitions.
b) the associated matrix $A$ is:
$A= \begin{pmatrix} -1 & 0 & 0\\ -2 & 2 & 1 \\ 2 & 0 & 1 \\ \end{pmatrix} $
c) used the fact that the dimension is equal to 3 and have proven they are linearly independent by showing that $C_o=C_1=C_2=0$.
And here is where i get stuck. Any help would be appreciated.
d)
$$\mathcal{C}=\left( \begin{array}{ccc} 0 & -1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & -1 \\ \end{array} \right)$$ $$\mathcal{C}\cdot \mathcal{B}=(x^2-x,x,-x^2+x+1)$$ $$\mathcal{C}^{-1}=\left( \begin{array}{ccc} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ \end{array} \right)$$ $$\mathcal{C}^{-1}\cdot (x^2-x,x,-x^2+x+1)=(1,x,x^2)$$