(3 points) Let P, denote the vector space of polynomials in the variable x of degree or less with real coefficients. Let

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3 Points Let P Denote The Vector Space Of Polynomials In The Variable X Of Degree Or Less With Real Coefficients Let 1 (25.9 KiB) Viewed 76 times

(3 points) Let P, denote the vector space of polynomials in the variable x of degree or less with real coefficients. Let DP: P → P, be the function that sends a polynomial to its second derivative. That is, D ((x)) = " (x) for all polynomials p(x) E P. Da linear transformation? Let p(x) = ax + ax + ax + ao and g(x) = byx' + b2x +bx+bo be any two polynomials in P, and c ER. = do a. D ((*)+(x)) = 6a 3V+Vb_3V)x+2Na_2V+Yb_29) (Enter a, as a3, to.) D (p(x)) + D ((x)) = 6{a_3Vx+242_20 + 64b_3\x+2Vb_20 Does Dº (p(x) + 4(x)) = D (p(x)) + D (@(x)) for all p(x),(x) E P? Yes, they are equal b. Dcp(x)) = 6Va_3Vxc+24a_2°C (D (p(x))) = 6/A_3\x*240 20 Does D (cp(x)) = c(D(x) for all c € R and all p(x) € Pj? Yes, they are equal C.In Da linear transformation? f is a linear transformation