Let B = {} and B' = {} for two bases in $\displaystyle \Re^3$, and suppose that the transition matrix from B' to B is

P = $\displaystyle \begin{pmatrix}1 & -1 & 2 \\ 0 & 1 & 2 \\ 3 & 0 & -1 \end{pmatrix}$

find $\displaystyle u_1$ and $\displaystyle u_2$ as linear combinations of $\displaystyle v_1$,$\displaystyle v_2$,$\displaystyle v_3$