# Finding the transition matrix

1. Mar 23, 2017

### Lord Anoobis

1. The problem statement, all variables and given/known data
Let $B_1 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 0 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 0\\ 0 \end{bmatrix}}, {\begin{bmatrix} 0 \\ 0 \\ 1\\ 1 \end{bmatrix}}$ and $B_2 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 1 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 1\\ -1 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ -1\\ 1 \end{bmatrix}}$ be two bases for $span(B_1)$, where the usual left to right ordering is assumed. Find the transition matrix $P$B1$\to$B2

2. Relevant equations

3. The attempt at a solution
I'm a bit flummoxed here. All the problems I've dealt with so far have had $n$ $n \times 1$ vectors and were solved by finding inverses. That cannot work here. What would be the first step in solving this?

2. Mar 23, 2017

### PeroK

You could express one set of basis vectors in terms of the other basis.

3. Mar 23, 2017

### Lord Anoobis

Would you happen to know how to get formulas to display correctly on an android phone? I'm away from my pc for a spell and I can't see much this way.

4. Mar 23, 2017

### Math_QED

The first step: know the relevant definitions and theorems

If you want to find the transition matrix, you have to know what information can be found within it. In general, a transition matrix gives you all the information you need to know to convert coordinates of a certain basis to coordinates relative to another basis. Denote the transition matrix from $B_1$ to $B_2$ with $M$. Do you know what information you can find in the columns of $M$?