Question

Solve the following system of equations using an augmented matrix and Gauss-Jordan Elimination. Be sure to show your work and explain what you are doing. Then, interpret your answer in terms of the original system.

Answer 1

Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

`\begin{gathered} \begin{bmatrix}3x+2y-4z=4 \\ x-3y-10z=8 \\ -5x-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}(4-2y+4z)/(3)-3y-10z=8 \\ -5\cdot(4-2y+4z)/(3)-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}(-11y-26z+4)/(3)=8 \\ (-2y+16z-20)/(3)=-2\end{bmatrix} \\ \begin{bmatrix}(-2\left(-(26z+20)/(11)\right)+16z-20)/(3)=-2\end{bmatrix} \\ \begin{bmatrix}(4\left(19z-15\right))/(11)=-2\end{bmatrix} \\ y=-(26\cdot(1)/(2)+20)/(11) \\ y=-3 \\ x=(4-2\left(-3\right)+4\cdot(1)/(2))/(3) \\ x=4 \\ \end{gathered}`

Finally we obtain that the solution to the system is:

`x=4,\: z=(1)/(2),\: y=-3`