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## Homework Statement

Linear transformation T: P

_{2}->P

_{2}

T(f) = -5f + 8f'

Need to find detA (A is a matrix of T)

## Homework Equations

T(f) = Af

## The Attempt at a Solution

The basis of P

_{2}is B={1, x, x

^{2}}. Some polynomial f with respect to B looks like this in general:

(a, b, c)

^{T}

right? So, T(f) = -(a, b, c)

^{T}+ 8 (0, b, 2c)

^{T}= (-a, 7b, c)

^{T}.

So, A*(a, b, c)

^{T}= (-a, 7b, c)

^{T}, therefore A =

1 0 0

0 7 0

0 0 1

And detA = -7. This is how I was thinking about it, but the answer is wrong and I am confused :(