6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2 = (1, 1,0). (i) Find the 3 x 3 projection matrix P onto S. (ii) Show that P2 = P. (iii) Find a vector whose projection onto S is the zero vector. (iv) Show that I - P projects onto the line perpendicular to S.

Plz

Find three vectors v1, v2, v3 such that (1) any two span a plane, and (2) Span{v1, v2, v3} is also a plane. v1 = v2 = V3 =

#1) Find the projection of U = ( 3 -5 ) onto V = ( 6, 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU.#2) Find the projection of U = ( 3 4 ) onto V = ( 8, 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU#3)Find the projection of U = ( 2 , 2 ) onto V = ( 6, 1 ) . Then write U as the sum of two orthogonal vectors one which is projvU2))#4)Find the projection of U = ( 4 , 2 ) onto V = ( 1 ,- 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU3)