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posted by  lisa676 on 8/27/2008 9:30:06 AM  |  status: Live  

Find matrix from the bases

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Let V and V¢ be vector spaces with bases B = {e1, e2, e3 } and B¢ = {e¢1, e¢2, e¢3, e¢4 }, respectively.

Furthermore, let T: V ® V¢ be a linear transformation such that
T(e1)= 4e'1+4e'2
T(e2)= -2e'1+6e'2+5e'3-4e'4
T(e3)= -2e'1-2e'2-4e'3+5e'4

Determine the matrix A of T w.r.t. the bases B and B¢.

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posted by dkg on 8/27/2008 2:05:51 PM  |  status: Live
Asker's Rating: Lifesaver   
lisa676's comment:
"thanks!"
Response Details:
For T:V -> V',
The transformation vector is given by
 
[T(e1) T(e2) T(e3)]  = A where T(ej) is the corresponding vector is V' for ej.
 
The coordinate vector is V is transformed to that in V' as follows
Observing the equations , we get
A =
Hope this helps ... 
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