Suppose T is a linear transformation, where ū (1, 0, 0) V = = W = (0, 1, 0) (0, 0, 1) Find the following: T(3ū+ 6 + 8u): = T(3, 4, 1)) = T(u) T(v) T(w) = (1, -3) (3, 1) (3, 3) (Enter vectors (x, y) using < x, y>) SUBMIT A PHOTO OF YOUR HANDWRITTEN WORK HERE. (Enter vectors (x, y) using < x, y >)

Suppose T: R2-→R³ is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(-3U-2V). 14 18 U = V = T(U) = -7 T(V) =-9 3 16 21 T(-3U–2V) = | 0

(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 - 2v. Compute (T. T)(v), where TT is the composition of T with itself. Express your answer as a linear combination of u and v. (ToT)(v) = 10 u + -1 V Incorrect answer. Incorrect answer. (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(4v+3w) = -2v-2w and T(v+1w) = 5v+2w. Compute T(v) and express it as a linear combination of v and w. T(v) = 4 v + 2 W Incorrect answer. Incorrect answer.

Suppose T is a linear transformation, where (1, 0, 0) T(u) T(7) (0, 1,0) W (0,0,1) T(w) Then I can be represented by the matrix ū V = = = T= = = = (5, -3, -2) (-2,-1,0) (0,5, 4)