(a) Let u and v be (fixed, but unknown) vectors in R". Suppose that T : R" - R" is a linear transformation such that T(u) = 7utv and T(v) = 5u - 3v. Compute (T o T) (v), where To T is the composition of T with itself. Express your answer as a linear combination of u and v. ( T O T ) ( V ) = u + (b) Let v and w be (fixed, but unknown) vectors in R", which are not scalar multiples of each others. Suppose that T : R" - R" is a linear transformation such that T(-2v-3w) = 2v+3w and T(v+1w) =-2v+3w. Compute T(v) and express it as a linear combination of v and w. T( v ) = V WDefine the characteristic polynomial of a matrix A as pA(m) = det(;cI A). Then find the characteristic polynomial of the matrix 6 6 12 A = 3 9 12 3 6 9 pA(x) = lformat: a*(X'l)*(x2)*(X3) l Your last answer was interpreted as follows: a,~(;c1)-(:v2)-(w3) The variables found in your answer were: [(1, :17]