- #1

Rifscape

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Member warned about posting with no effort shown

## 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.