MAT223 Lecture 05

MAT223 Readings 02
MAT223 PCRA 1

• 1
  • If a System of Linear Equations is Inconsistent. Then the Reduced Row Echelon Form must have the rightmost column containing a leading one.
• 2
  • If we have a solution $\left[\begin{array}{c}-1+2s-t\\ 2+3s-5t\\ s\\ t\end{array}\right]$ then the basic solutions?
  • Extract into particular and parameterised.
  • $\left[\begin{array}{c}-1\\ 2\\ 0\\ 0\end{array}\right]+s\left[\begin{array}{c}2\\ 3\\ 1\\ 0\end{array}\right]+t\left[\begin{array}{c}-1\\ -5\\ 0\\ 1\end{array}\right]$
• 3
  • $\left[\begin{array}{ccccc}1& 0& -2& 3& 0\\ 0& 1& 3& -2& 0\end{array}\right]$
  • $x_1-2x_3+3x_4=0$
  • $x_2+3x_3-2x_4=0$
  • $x_1=2x_3-3x_4$
  • $x_2=-3x_3+2x_4$
  • $x_3=s$
  • $x_4=t$
  • $x_1=2s-3t$
  • $x_2=-3s+2t$
  • $(s,t)=(0,0)$
  • $\left[\begin{array}{c}0\\ 0\\ 0\\ 0\end{array}\right]+s\left[\begin{array}{c}2\\ -3\\ 1\\ 0\end{array}\right]+t\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$