Question

Let Pk denote the vector space of all polynomials with degree less than or equal to k. Define a linear transformation T : P4 ! P3 by T(f(x)) = f(0)+f '1)(x-1)+f ''(2)(x-2)^2+f'''(3)(x-3)^3. Find the matrix representation for T relative to the standard basis {1; x; x^2; x^3; x^4} of R4 and the reversed standard basis {x^3; x^2; x; 1} of R3.

Answer 1

Answer:

Step-by-step explanation:

T(1)=1=0*x^3 0*x^2 0*x 1*1 T(x)=x-1=0*x^3 0*x^2 1*x (-1)*1 T(x^2)=2x^2-6x 6=0*x^3 2*x^2 (-6)*x 6 T(x^3)=6x^3-48*x^2 141*x-141 T(x^4)=24*x^3-204*x^2 628*x-604*1 collect the coefficient matrix and take its transpose

0 0 0 6 24

0 0 2 -48 -204

0 1 -6 141 628

1 -1 6 -141 -604