Find a preimage of the vector H V= under the linear transformation T given by the matrix -3] 14 A = L-4 -4 That is find the vector u such that T(u) = v. ū₁ U₂

5. Find the orthogonal projection of the vector b = vectors V₁ = -1- and v2 = onto the subpace E spanned by the (Note that v₁ V₂).

Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + v2, 2v,), v = (6, 3, 0), w = (-7, 3, 10) (a) the image of v (-3,9,12) (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.) (3,10,t)

Let S be the parallelogram then determine the area of parallelogram by the vectors [h | 1 and let A = h and [0 h+1] h=102 Also compute the area of the image of parallelogram under the linear transformation ""