- #1
JamesGoh
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Homework Statement
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]
Homework Equations
T(u+v)= T(u) + T(v)
λT(v) = T(λv)
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 ?