I have 2/3 parts worked out but I'm not getting the correct answer for the 3rd. Any help is appreciated!
Consider the bases B={u1,u2} and B'={u'1,u'2} for R2, where
u1=[2
2],
u2=[4
-1],
u'1=[1
3],
u'2=[-1
-1]
(a) Find the transition matrix from B' to B and I got
[13/10 -1/2]
[-2/5 0 ]
(b) Find the transition matrix from B to B' and I got
[0 -5/2]
[-2 -13/2]

Both checked out in the answers section.
Now my problem is:
(c) Compute the coordinate vector [w]B, where
w=[3
5]
The answer is:
[-17/10
8/5 ] I just need help figuring out how to calculate that.

Question

I have 2/3 parts worked out but I'm not getting the correct answer for the 3rd. Any help is appreciated!  
Consider the bases B={u1,u2} and B'={u'1,u'2} for R2, where 
u1=[2  
       2], 
u2=[4  
       -1], 
u'1=[1  
        3], 
u'2=[-1  
       -1]
(a) Find the transition matrix from B' to B and I got 
      [13/10   -1/2]
      [-2/5         0  ]
(b) Find the transition matrix from B to B' and I got
 [0        -5/2]
 [-2    -13/2]

Both checked out in the answers section.
Now my problem is:
(c) Compute the coordinate vector [w]B, where 
w=[3
      5]
The answer is: 
[-17/10
      8/5 ]  I just need help figuring out how to calculate that.

anonymous · Answer

I've got it figured out...