Linear Algebra and Its Applications · Problem 3.1.7

Orthogonality — Gilbert Strang

Mathematics · orthogonal-vectors-subspaces

Problem

Find a vector

x

orthogonal to the row space of

A

, and a vector

y

orthogonal to the column space, and a vector

z

orthogonal to the nullspace:

A = \begin{bmatrix}1 & 2 & 1\\2 & 4 & 3\\3 & 6 & 4\end{bmatrix}.