Question: (a) Let u and v be (fixed, but unknown) vectors in R. Suppose that T' : R > R is a linear transformation such that

(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) = 6u +v and T(v) =4u -3v. Compute (To 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" is a linear transformation such that T(7v+6w) =3v-3w and T(v+1w) =3v+2w. Compute T(v) and express it as a linear combination of v and w. T(v) = W

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