Let V be a vector space, v, u E V, and let T₁ : V → V and T₂ : V → V be linear transformations such that T₁ (v) = 2v4u, T₁ (u) = -7v+2u, T₂ (v) = 4v +2u, T₂ (u) = 6v - 3u. Find the images of v and u under the composite of T₁ and T₂. (T₂T₁)(v) = (T₂T₁)(u) =

Let V be a vector space, v, u E V, and let T₁ : V → T₁ (v) = 5v +6u, T₂ (v) = 4v 4u, Find the images of v and è under the composite of T₁ and T₂. (T₂T₁)(v) = (T₂T₁)(u) = - V and T₂ : V → V be linear transformations such that T₁(u) = −3v - 3u, T₂(u) = 6v+6u.

(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.

Let V be a vector space, v, u € V, and let T₁: V → V and T2 VV be linear transformations such that T₁(v) = 6v 2u, T₁(u) = −2v + 4u, T₂ (v) = -2v 2u, T₂(u) = -7v+2u. Find the images of vand u under the composite of T₁ and T₂. (T₂T₁)(v) = (T₂T₁)(u) =