- #1
kehler
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Homework Statement
Let B & C be the following subsets of R^2
B= {[3 1] , [2 2]} (the vectors should be in columns instead of rows)
C= {[1 0] , [5 4]}
Let T: R^2 -> R^2 be the linear transformation whose matrix with respect to the basis B is
[2 1]
[1 5] (the brackets should be joint, it's a 2 x 2 matrix)
Find the matrix T with respect to C. Check your answer by finding the determinant and the trace of each matrix.
The Attempt at a Solution
I found the change of basis matrix from B to C to be
[(7/4) (-2/4)]
[(1/4) ( 2/4) ] (again a 2x2 matrix)
I did this by multiplying the change of basis matrix from the standard basis to C, with the change of basis matrix from the B basis to the standard matrix like this:
[1 (-5/4)] [3 2]
[0 (1/4)] [1 2]
I then multiplied the given matrix by the change of basis matrix from B to C to get
[3 (-3/4)]
[1 (11/4)]
I thought my answer was correct but the trace for the matrix I got is 8.25 whilst the trace of the original matrix is 7. They should be the same, right??
Can anyone see where I went wrong? I'm not sure if I got the change of basis matrices right :S. The columns of the set B should form the change of basis matrix from B to the standard basis, shouldn't they?
Any help would be appreciated :)