The vectors a 1 = (1, 1, 0) T , a 2 = (1, 1, 1) T span a two-dimensional plane S which is a subspace of R 3 . a) Find an orthonormal basis for S . b) Find the projection matrix P which projects onto...

The vectors

a


₁

= (1, 1, 0)
^T
,

a
₂

= (1, 1, 1)
^T

span a two-dimensional
plane
S
which is a subspace of
R
³.

a) Find an orthonormal basis for
S.

b) Find the projection matrix
P
which projects onto the plane.

c) Find a non-zero vector in
R
³
that is projected to zero.