Linear Algebra and Its Applications · Problem 3.1.12

Orthogonality — Gilbert Strang

Mathematics · orthogonal-vectors-subspaces

Problem

Find a basis for the orthogonal complement of the row space of

A

A = \begin{bmatrix}1 & 0 & 2\\1 & 1 & 4\end{bmatrix}.

Split

x = (3,3,3)

into a row space component

x_r

and a nullspace component

x_n