## Question

###### Let Pn be the vector space of polynomials of degree atmOST " In the problems below , let V = Nul(E), where E P R? is E(p) Let $ = {1,4,02,08,1'} be the standard hasis fo1 P; and let Ps R' _ P be the 'linear combinatins o[ S' linear transformation Let [Js + Rihe its inverse the cvorinates with respect to $ linAr trasformatiomFindl the 2 x 5 matrix A ; R' VP ER?,2. Fiudl a hasis for Nul(A).Apply Ps to the vectors our hasis for Nul(A) to show that 8 = [2 _ 2t+4,7'

Let Pn be the vector space of polynomials of degree atmOST " In the problems below , let V = Nul(E), where E P R? is E(p) Let $ = {1,4,02,08,1'} be the standard hasis fo1 P; and let Ps R' _ P be the 'linear combinatins o[ S' linear transformation Let [Js + Rihe its inverse the cvorinates with respect to $ linAr trasformatiom Findl the 2 x 5 matrix A ; R' VP ER?, 2. Fiudl a hasis for Nul(A). Apply Ps to the vectors our hasis for Nul(A) to show that 8 = [2 _ 2t+4,7' _ 3t+2,/' _ 4/+3] hasis for V, (Recall that V = Nul(E))

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