Exercise 13

Gauss’s Method works by combining the equations in a system to make new equations.

• Can we derive the equation $3x-2y=5$ by a sequence of Gaussian reduction steps from the equations in this system?

  $$\begin{array}{rcrcr}x&+&y&=&1\\ 4x&-&y&=&6\end{array}$$

• Can we derive the equation $5x-3y=2$ with a sequence of Gaussian reduction steps from the equations in this system?

  $$\begin{array}{rcrcr}2x&+&2y&=&5\\ 3x&+&y&=&4\end{array}$$

• Can we derive $6x-9y+5z=-2$ by a sequence of Gaussian reduction steps from the equations in the system?

  $$\begin{array}{rcrcrcr}2x&+&y&-&z&=&4\\ 6x&-&3y&+&z&=&5\end{array}$$