Linear Algebra and Its Applications · Problem 3.3.6

Orthogonality — Gilbert Strang

Mathematics · projection-onto-column-space

Problem

Find the projection of

b

onto the column space of

A

A = \begin{bmatrix} 1 & 1 \\ 1 & -1 \\ -2 & 4 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 2 \\ 7 \end{bmatrix}.

Split

b

into

p + q

, with

p

in the column space and

q

perpendicular to that space. Which of the four subspaces contains

q