Linear Algebra and Its Applications · Problem 3.3.14

Orthogonality — Gilbert Strang

Mathematics · projection-matrix-plane

Problem

The vectors

a_1 = (1, 1, 0)

and

a_2 = (1, 1, 1)

span a plane in

\mathbf{R}^3

. Find the projection matrix

P

onto the plane, and find a nonzero vector

b

that is projected to zero.