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March 24th, 2010, 08:11 PM   #1
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Representation Question

(note when I say a0 or a1 I mean alpha subscript 0 or alpha subscript 1: and when I say t i mean the math symbol that looks like a t (I think it's called tao)
define the mapping T from R4[t] to R4[t] by:
T(a0 + a1*t + a2*t^2 + a3*t^3)=a0 + a1*t + a2((1.5*t^2)-0.5) + a3((2.5*t^3)-1.5*t)
Let X=(1 , t , t^2 , t^3)
1.find A=RxxT. that A (and hence T) is nonsingular.
3. Find bases V and W such that RwxT and RxvT are each the identity matrix.
I am stuck, I tried doing number 1 but I am not sure if I am right: I got
a0 0 0 0
0 a1 0 0
a= -0.5*a2 0 1.5*a2 0
0 -1.5*a3 0 2.5*a3

(this being the matrix)

and I am not sure about the rest.
Thank you in advance.
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