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  • MAT223 Readings 01

Solutions as Columns in Linear Algebra

• It's convenient to store Solutions to a System of Linear Equations of $m\times n$ in a column of size $n$.
• If $x_1=c_1,x_2=c_2,\dots ,x_n=x_n$ then $\overrightarrow{x}=\left[\begin{array}{c}{c}_1\\ c_2\\ \dots \\ c_n\end{array}\right]$. where $\overrightarrow{x}$ is a solution.
• Ex:
  • $3\times 5$ system
  • $\left[\begin{array}{cccccc}1& 0& 0& 1& -2& 2\\ 0& 0& 1& 5& 6& 1\\ 0& 0& 0& 0& 0& 0\end{array}\right]$
  • $x_1=2-t+2u$
  • $x_2=s$
  • $x_3=1-5t-6u$
  • $x_4=t$
  • $x_5=u$
  • $\overrightarrow{x}=\left[\begin{array}{c}2-t+2u\\ s\\ 1-5t-6u\\ t\\ u\end{array}\right]$