Exercise 2

Each system is in echelon form. For each, say whether the system has a unique solution, no solution, or infinitely many solutions.

• (a)  $\begin{array}{rcrcr}-3x&+&2y&=&0\\ &&-2y&=&0\end{array}$     (b)  $\begin{array}{rcrcrcr}x&+&y&&&=&4\\ &&y&-&z&=&0\\ \end{array}$     (c)  $\begin{array}{rcrcrcr}x&+&y&&&=&4\\ &&y&&-z&=&0\\ &&&&0&=&0\end{array}$     (d)  $\begin{array}{rcrcr}x&+&y&=&4\\ &&0&=&4\end{array}$     (e)  $\begin{array}{rcrcrcr}3x&+&6y&+&z&=&-0.5\\ &&&&-z&=&2.5\\ \end{array}$     (f)  $\begin{array}{rcrcr}x&-&3y&=&2\\ &&0&=&0\end{array}$     (g)  $\begin{array}{rcrcr}2x&+&2y&=&4\\ &&y&=&1\\ &&0&=&4\end{array}$     (h)  $\begin{array}{rcrcr}2x&+&y&=&0\end{array}$     (i)  $\begin{array}{rcrcr}x&-&y&=&-1\\ &&0&=&0\\ &&0&=&4\end{array}$     (j)  $\begin{array}{rcrcrcr}x&+&y&-&3z&=&-1\\ &&y&-&z&=&2\\ &&&&z&=&0\\ &&&&0&=&0\end{array}$