Let be the linear transform defined by .

Let E and F be to bases: .

Determine the matrix representation, C, of T relative to E.

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My approach (don't know if it's correct):

Let f = .

which is sorta correct,except: The coords of relative to E are (c,b,a) not (a,b,c)! So if I'm given a vector X relative to E, CX won't be correct.

What should I have done?