Find the change of basis matrix from the basis {1,x,x2}\{1, x, x^2\}{1,x,x2} to {1,x−1,(x−1)2}\{1, x-1, (x-1)^2\}{1,x−1,(x−1)2} for P2P_2P2.
(1−1101−2001)\begin{pmatrix} 1 & -1 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \end{pmatrix}100−1101−21
(111012001)\begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix}100110121
(100110121)\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix}111012001
(1−1001−2001)\begin{pmatrix} 1 & -1 & 0 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \end{pmatrix}100−1100−21