coordinate matrix $[x]_B$. given the coordinate matrix $[x]_{B'}$
$B = \{(1, 3, 4), (2, -5, 2), (-4, 2, -6)\}$,
$B' = \{(-4, -192, -9), (-1, 64, 3), (3, -192, -8)\}$,
$[x]_{B'} = \begin{bmatrix} -1 \\ 0 \\ 2 \end{bmatrix}$
(a) Find the transition matrix from $B$ to $B'$.
$P^{-1} = \begin{bmatrix} 3/7 & -2/67 & -2/7 \\ 3/448 & 11/224 & 3/112 \\ 2 & -13 & 0 \end{bmatrix}$
(b) Find the transition matrix from $B'$ to $B$.
$P = \begin{bmatrix} \_ & \_ & \_ \\ \_ & \_ & \_ \\ \_ & \_ & \_ \end{bmatrix}$
(c) Verify that the two transition matrices are inverses of each other.
$P P^{-1} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
(d) Find the coordinate matrix $[x]_B$ given the coordinate matrix $[x]_{B'}$
