Exercise 3

Solve each system, giving the solution set in vector notation. Identify a particular solution and the solution of the homogeneous system.

• (a)  $\begin{array}{rcrcrcr}2x&+&y&-&z&=&1\\ 4x&-&y&&&=&3\end{array}$     (b)  $\begin{array}{rcrcrcrcr}x&&&-&z&&&=&1\\ &&y&+&2z&-&w&=&3\\ x&+&2y&+&3z&-&w&=&7\end{array}$     (c)  $\begin{array}{rcrcrcrcr}x&-&y&+&z&&&=&0\\ &&y&&&+&w&=&0\\ 3x&-&2y&+&3z&+&w&=&0\\ &&-y&&&-&w&=&0\end{array}$     (d)  $\begin{array}{rcrcrcrcrcr}a&+&2b&+&3c&+&d&-&e&=&1\\ 3a&-&b&+&c&+&d&+&e&=&3\end{array}$