Question

Let T:R3 + Rbe the linear transformation that projects vectors orthogonally into the vector v = 3 In other words, TⓇ) = proj, Use the formula for projections to compute each of the following: TO) = proj; i = TG) = proj;j = T(K) = proj;k = Use these results to determine the terms of the corresponding matrix A:

Answer 1

As proj u = 2 4 v. Here Tal= Projne To 2v, y) = 1 + 1 + 1 = || find a Clio, o TO) = Proj 7 - Luis <vvy < 6130T, Chioso) 1131 T(J) = Prof J CV, 5) Lviv> AS J =(0,1,0). cv, J) = C(1,311ST, coil,oT> TJ) = Proj J = 3 -113 بما k=,0,1) T(E) - Proj F = ZVIES 3 v Vivy Lvie) = 2ca1311)T,Co,o, 1 = 1 T(E)= Projit - I lt -

Corresponding O po mehix A 3 93