(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the following defined transformation

[itex]T(a + bt+ct^{2}) = (a+c) - (c+b)t + (a+b+c)t^{2} [/itex]

find the matrix with respect to the standard basis

From my understanding, the standard basis for a 3 element vector would

be

[itex](0,0,1)^{T} (0,1,0)^{T} (1,0,0)^{T}[/itex]

2. Relevant equations

T(u+v)= T(u) + T(v)

λT(v) = T(λv)

3. The attempt at a solution

okay, if I used the defined transformation, I get the following when I put any of the standard basis into the transformation

[itex]T(0,0,1)^{T}=1 - t + t^{2}

T(0,1,0)^{T} = 0 -t + t^{2}

T(1,0,0)^{T} = 1 - 0 + t^{2}

[/itex]

If I am correct, the matrix should be the following

1 -1 1

0 -1 1

1 0 1

However, the tutorial answers have it in the form

1 0 1

-1 -1 0

1 1 1

Shouldn't my answer be correct, since the [itex]t[/itex] and [itex]t^{2}[/itex] terms are different parts of a linear equation which is why they can't be in the same column ?

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# Homework Help: Linear transformations + writing of output matrix

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