Clu Linear Algebra Ch 1 S1 Examples

Example Question

Solve each system by using elementary row operations on the equations or on the augmented matrix

(1)
\begin{matrix} x_1+5(x_2)=7 \end{matrix}
(2)
\begin{matrix} -2(x_1)-7(x_2)=-5 \end{matrix}

The matrix

(3)
\begin{matrix} 1 & 5 & | & 7 \\ -2 & -7 & | & -5 \\ \end{matrix}

The matrix row reduced to

(4)
\begin{matrix} 1 & 0 & | & -8 \\ 0 & 1 & | & 3 \\ \end{matrix}
(5)
\begin{matrix} x_1+0(x_2)=-8\\ x_1 =-8 \end{matrix}
(6)
\begin{matrix} 0(x_1)+1(x_2)=3\\ (x_2)=3 \end{matrix}

The Solution is ($x_1$,$x_2$)=($-8$,$3$)

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