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Rifscape
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Homework Statement
Consider the linear transformation T from
V = P2
to
W = P2
given by
T(a0 + a1t + a2t2) = (−4a0 + 2a1 + 3a2) + (2a0 + 3a1 + 3a2)t + (−2a0 + 4a1 + 3a2)t^2
Let E = (e1, e2, e3) be the ordered basis in P2 given by
e1(t) = 1, e2(t) = t, e3(t) = t^2
Find the coordinate matrix [T]EE of T relative to the ordered basis E used in both V and W, that is, fill in the blanks below: (Any entry that is a fraction should be entered as a proper fraction, i.e. as either x/y or -x/y where x and y are positive integers with no factors in common.)
T(e1(t)) = _e1(t) + _ e2(t) + _e3(t)
T(e2(t)) = _e1(t) + _e2(t) + _e3(t)
T(e3(t)) = _e1(t) + _e2(t) + _e3(t)
and therefore :
[T]EE = the combined matrix of the coefficients of the above three equations.
Sorry for the poor formatting
Homework Equations
No idea
The Attempt at a Solution
I have no idea
I have no idea how to do this, if someone can give me a step by step solution so that I can understand each step and process I would appreciate it greatly.
Thanks for your help.