Science:Math Exam Resources/Courses/MATH307/April 2006/Question 05 (c)/Statement

A matrix A and a vector b are given by

$A=\left[\begin{array}{cc}1& 0\\ 1& 1\\ 0& 1\end{array}\right]$

$b=\left[\begin{array}{c}2\\ 3\\ 4\end{array}\right]$

Split b into $b=b^{\perp }+b^{\parallel }$, where $b^{\parallel }$ is in R(A) and $b^{\perp }$ is in $R(A{)}^{\perp }$ (i.e. the orthogonal complement of R(A).)