Linear Algebra and Its Applications · Problem 3.2.11

Orthogonality — Gilbert Strang

Mathematics · cosines-projections-onto-lines

Problem

(a) Find the projection matrix

P_1

onto the line through

a = \begin{bmatrix}1\\3\end{bmatrix}

and also the matrix

P_2

that projects onto the line perpendicular to

a

. (b) Compute

P_1 + P_2

and

P_1P_2

and explain.