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  • MAT223 Lecture 02

Solutions to a System of Linear Equations

• A solution is a choice of numbers $s_1,s_2,\dots ,s_n$ which when substituted for $x_1,x_2,\dots ,x_n$ it makes the equation true.
• $c_1{x}_1+c_2{x}_2+\cdots +c_n{x}_n=b$ turns into $c_1{s}_1+c_2{s}_2+\cdots +c_n{s}_n=b$
• Example:
  • $\begin{array}{c}x=2\\ y=1\\ z=1\end{array}$ is a solution to $x-2y+z=1$ because we get:
  • $\begin{array}{cc}\text{LHS}& \text{RHS}\\ (2)-2(1)+1=1& 1\\ ✓& ✓\end{array}$