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!
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 $\displaystyle w_1=1v_1-1v_2$ and $\displaystyle w_2=2v_1-0v_2$
Which gives
$\displaystyle w_1=(-2,-2)$
$\displaystyle w_2=(2,-4)$