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March 24th, 2010, 08:11 PM  #1 
Senior Member Joined: Sep 2009 Posts: 115 Thanks: 0  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. 2.show 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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