Let Riz be a linear space of all polynomials p(x) = ar²+bx+c (a,b,c & R) whose degree is no more than 2 and R³ be a linear space of all real vectors [9,9₂,93 (9.₂₂ € R) with the standard operations of addition and scalar multiplication. Let L be the transformation from Rz to R³ defined by L(p(x)) = [p(1), p(0), p(-1)]. (1) Prove that L is a linear transformation; ) Find the matrix A representing I with respect to the basis {1,1, ²} and •C Find the Kernel of the linear transformation L, denoted by Ker(L); Is the matrix A diagonalizable? Why?

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