Let S (1,2,3) and T: Fun(S) R* be the linear transformation defined by T(f(2)) = (4f(3)-3f(2),...

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Let S (1,2,3) and T: Fun(S) R* be the linear transformation defined by T(f(2)) = (4f(3)-3f(2), f(1)-f(2), 3f(1)-4f(3), 31(1)+31(2)-8f(3)) Find bases for Ker(7) and Im(T). Basis of Ker(7) = {} Basis of Im(7)= {} Enter functions using characteristic funtions, writing x1 for x etc. Tertial credit on this problem. 4 Let S (1,2,3) and T: Fun(S) R* be the linear transformation defined by T(f(2)) = (4f(3)-3f(2), f(1)-f(2), 3f(1)-4f(3), 31(1)+31(2)-8f(3)) Find bases for Ker(7) and Im(T). Basis of Ker(7) = {} Basis of Im(7)= {} Enter functions using characteristic funtions, writing x1 for x etc. Tertial credit on this problem. 4