# Math Help - basis

1. ## basis

let S = { v1 , v2} T = { w1, w2} be bases for R2

Given: V1 = ( 1, -2) V2= ( 3, 0)

Transition matrix from T to S be
[ 1 2 ]
[-1 0]

Find w1 and w2.

Please help me with the steps. I am not sure where to start!! Thanks!

2. The column vectors of your matrix (1,-1) and (2,0) are the coordinates of w1 and w2 on respect to the basis S.
It means that $w_1=1v_1-1v_2$ and $w_2=2v_1-0v_2$
Which gives
$w_1=(-2,-2)$
$w_2=(2,-4)$