Exercise 4

Solve each system using matrix notation. Express the solution using vectors.

• (a)  $\begin{array}{rcrcr}3x&+&6y&=&18\\ x&+&2y&=&6\end{array}$     (b)  $\begin{array}{rcrcr}x&+&y&=&1\\ x&-&y&=&-1\end{array}$     (c)  $\begin{array}{rcrcrcr}x_{1}&&&+&x_{3}&=&4\\ x_{1}&-&x_{2}&+&2x_{3}&=&5\\ 4x_{1}&-&x_{2}&+&5x_{3}&=&17\end{array}$     (d)  $\begin{array}{rcrcrcr}2a&+&b&-&c&=&2\\ 2a&&&+&c&=&3\\ a&-&b&&&=&0\end{array}$     (e)  $\begin{array}{rcrcrcrcr}x&+&2y&-&z&&&=&3\\ 2x&+&y&&&+&w&=&4\\ x&-&y&+&z&+&w&=&1\end{array}$     (f)  $\begin{array}{rcrcrcrcr}x&&&+&z&+&w&=&4\\ 2x&+&y&&&-&w&=&2\\ 3x&+&y&+&z&&&=&7\end{array}$