Computeing the coordinate vector

[savageqm]

hello, am confuse with this problem.

I have

B = {U1,U2} and B' = {u'1,u'2}

u1 = [2,2], u2 =[4,-1] u'1 = [1,3], u'2 = [1,1]

Now I have found the transition matrix from B' to B which is

13/10 -1/2

-2/5 0

Now, the question that am having trouble with is: Compute the coordinate vector [w]B where

w = [3,-5]

What I did was.

[ 13/10 -1/2

-2/5 0 ] * [3,-5] = [32/5, -6/5]but, this answer is wrong according to my book. Please help explain what they are asking for. I figure they were asking for : [v]b = Pb' -> b[v]b'

the book answer is [w]B = [-17/10, 8/5]

opps I spelled computing wrong, sorry.

 

[Outlined]

w is not written in the basis B' but in the standard basis (1, 0) and (0, 1). Your book gives the correct answer.