Chapter 9.3, Problem 16E

Let $A=\left[\begin{array}{ccc}2& -1& 1\\ -1& 2& 1\\ 1& 1& 2\end{array}\right]$

a. Show that A is singular.

b. Show that $Ax=\left[\begin{array}{c}3\\ 1\\ 3\end{array}\right]$ has no solution.

c. Show that $Ax=\left[\begin{array}{c}3\\ 0\\ 3\end{array}\right]$ has infinitely many solutions.