Hi guys I have the following system of linear equations as shown below
$$-8y_1 + 5y_2 + 0y_3 = -2.8052$$
$$3y_1 + -8y_2 + 5y_3 = 0.1516$$
$$0y_1 + 3y_2 -8y_3 = -19.8819$$
I decided to use Gauss Jordan elimination method to solve for the variables
$$ \begin{matrix} -8 & 5 & 0 & | & -2.8052 \\ 3 & -8 & 5 & | & 0.1516\\ 0 & 3 & -8 & | & -19.8819\\ \end{matrix} $$
I decided to reduce R2 by using the folloiwng operation - R2 -----> $\frac{3}{8}$R1+R2 which givs the following
$$ \begin{matrix} -8 & 5 & 0 & | & -2.8052 \\ 0 & -6.125 & 5 & | & -0.9004\\ 0 & 3 & -8 & | & -19.8819\\ \end{matrix} $$
Then to further reduce the R3 -----> $\frac{3}{6.125}R2+R3$
$$ \begin{matrix} -8 & 5 & 0 & | & -2.8052 \\ 0 & -6.125 & 5 & | & -0.9004\\ 0 & 0 & -5.551 & | & -20.3229\\ \end{matrix} $$
Solving for $y_1,y_2,y_3$ gives the following
$$-5.551y_3 = -20.3229$$ $$y_3 = 3.6611$$
$$-6.125y_2 = -0.9004 +(-5(3.6611))$$ $$y_2 = 3.1357$$
$$-8y_1 = -2.8052 +(-5(3.1357))$$ $$y_1 = 2.3105$$