9. Let W be the subspace of P2 spanned by S = {P1, P2, P3, P4}...

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9. Let W be the subspace of P2 spanned by S = {P1, P2, P3, P4} where p₁ =1+3x+3x² P₁ = x+4x², p₁ = 5+6x+3x², P4 = =7+2x-x². a) Find a subset of S which is a basis for W. b) Express the element(s) of S not in the basis you found in part a) as linear combinations of the basis elements. - c) (Independent from parts a) and b)) Determine whether T(x, y) = (x,2y − 3) is a linear operator. 9. Let W be the subspace of P2 spanned by S = {P1, P2, P3, P4} where p₁ =1+3x+3x² P₁ = x+4x², p₁ = 5+6x+3x², P4 = =7+2x-x². a) Find a subset of S which is a basis for W. b) Express the element(s) of S not in the basis you found in part a) as linear combinations of the basis elements. - c) (Independent from parts a) and b)) Determine whether T(x, y) = (x,2y − 3) is a linear operator.

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a To find a basis for the subspace W spanned by S p1 p2 p3 p4 we need to check for linear independen... View the full answer