Finding the Transition Matrix and Coordinates with Respect to a Different Basis

[thatguythere]

Homework Statement

Let B = {(1,1,1),(1,2,2),(2,3,4)} be an ordered basis of R³, and let B` be the standard basis of R³.

Find the transition matrix from B to B` and use it to find the coordinates of (1,2,3)^T with respect to B.

Homework Equations

The Attempt at a Solution

Is it correct to apply the following?
u1 = 1(u`1) + 1(u`2) + 1(u`3)
u2 = 1(u`1) + 2(u`2) + 2(u`3)
u3 = 2(u`1) + 3(u`2) + 4(u`3)

 

[Fredrik]

How is the transition matrix from B to B' defined? If it's defined the way I think, you should express the primed basis vectors in terms of the unprimed, not the other way round.