# Find basis B given the transition matrix and B'

1. Apr 6, 2015

### fattycakez

1. The problem statement, all variables and given/known data
The Matrix P =
1 0 3
1 1 0
0 3 1
is the transition matrix from what basis B to the basis B' = {(1,0,0),(1,1,0),(1,1,1) for R3?

2. Relevant equations
[v]B=P[v]B'

3. The attempt at a solution
I'm looking at a theorem in my book that says

" if P is the transition matrix from a basis B' to a basis B for a finite-dimensional vector space V, then P is invertible and P-1 is the transition matrix from B to B'. "

So does the inverse of P give the basis B? Please tell me how wrong I am :)

2. Apr 7, 2015

### BiGyElLoWhAt

I will gladly tell you how wrong you are. Not at all (if I understand you correctly)
You have $\bf{P} \cdot \bf{B} = \bf{B'}$ Multiply both sides by $\bf{P}^{-1}$ and you have solved your equation for B.

3. Apr 7, 2015

### fattycakez

Awesome, thank you! \m/

4. Apr 8, 2015

No problemo