Let T: P P be the linear trasformation T(ao + ax + ax) = (ao...

 

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Let T: P₂ → P₁ be the linear trasformation T(ao + a₁x + a₂x²) = (ao + a₁)-(2a₁ + 3a₂)x a) Find the matrix fort he linear transformation T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and P₁. b) Verify that the matrix [T] B,B obtained in part (a) satisfies [T] BB [X]B = [T(X)]B, for every vector x = Co + C₁x + C₂2x² in P₂. Let T: P₂ → P₁ be the linear trasformation T(ao + a₁x + a₂x²) = (ao + a₁)-(2a₁ + 3a₂)x a) Find the matrix fort he linear transformation T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and P₁. b) Verify that the matrix [T] B,B obtained in part (a) satisfies [T] BB [X]B = [T(X)]B, for every vector x = Co + C₁x + C₂2x² in P₂.

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To find the matrix for the linear transformation T relative to the standard bases B 1 x x and B 1 x ... View the full answer