- #1
psychosomatic
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Homework Statement
Find the matrix representations [T][itex]\alpha[/itex] and [T]β of the following linear transformation T on ℝ3 with respect to the standard basis:
[itex]\alpha[/itex] = {e1, e2, e3}
and β={e3, e2, e1}
T(x,y,z)=(2x-3y+4z, 5x-y+2z, 4x+7y)
Also, find the matrix representation of [T][itex]^{\alpha}_{\beta}[/itex]
Homework Equations
None
The Attempt at a Solution
T(e1) = (2, 5, 4)
T(e2) = (-3, -1, 7)
T(e3) = (4, 2, 0)
So, I got [T][itex]\alpha[/itex] = (T(e1), T(e2), T(e3))
but for [T]β, I got [T]β=(T(e3), T(e2), T(e1))
However, the answers in the back of the book tell me that although my order for [T]β is correct, the vectors themselves are inverted.
ie: T(e1) = (4, 5, 2)
Why is this? And I'm not sure how to start the second half of the question...