Let $P = \begin{bmatrix} 2 & 3 & -1 \\ -4 & -5 & 0 \\ 5 & 6 & 1 \end{bmatrix}$, $v_1 = \begin{bmatrix} -3 \\ 4 \\ 3 \end{bmatrix}$, $v_2 = \begin{bmatrix} -8 \\ 4 \\ 3 \end{bmatrix}$, and $v_3 = \begin{bmatrix} -7 \\ 2 \\ 6 \end{bmatrix}$. Complete parts (a) and (b).
a. Find a basis $\{u_1, u_2, u_3\}$ for $\mathbb{R}^3$ such that $P$ is the change-of-coordinates matrix from $\{u_1, u_2, u_3\}$ to the basis $\{v_1, v_2, v_3\}$. [Hint: What do the columns of $P$ represent?]
$u_1 = \boxed{}$, $u_2 = \boxed{}$, $u_3 = \boxed{}$
$C \leftarrow B$
