# Thread: Bases and transition matrix question

1. ## Bases and transition matrix question

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 $\displaystyle v_1$,$\displaystyle v_2$,$\displaystyle v_3$

2. Originally Posted by flaming
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 $\displaystyle v_1$,$\displaystyle v_2$,$\displaystyle v_3$
B must have 3 elements not 2. let $\displaystyle B=\{u_1,u_2,u_3 \}.$ then $\displaystyle u_j=Pv_j, \ 1 \leq j \leq 3.$ so we have: $\displaystyle u_1=v_1-v_2+2v_3, \ u_2=v_2 + 2v_3, \ u_3=3v_1-v_3.$