Question

Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination.

Answer 1

We will have the following:

$\begin{gathered} \left(\begin{array}{ccc|c}-2 & -3 & 1 & -4 \\ -4 & -2 & -2 & 0 \\ 3 & 3 & 1 & 2\end{array}\right)\rightarrow\left(\begin{array}{ccc|c}1 & 3/2 & 1/2 & 2 \\ -4 & -2 & -2 & 0 \\ 3 & 3 & 1 & 2\end{array}\right) \\ \\ \rightarrow\left(\begin{array}{ccc|c}1 & 3/2 & 1/2 & 2 \\ 0 & 4 & 0 & 8 \\ 3 & 3 & 1 & 2\end{array}\right)\rightarrow\left(\begin{array}{ccc|c}1 & 3/2 & 1/2 & 2 \\ 0 & 4 & 0 & 8 \\ 0 & -3/2 & -1/2 & -4\end{array}\right) \\ \\ \rightarrow\left(\begin{array}{ccc|c}1 & 3/2 & 1/2 & 2 \\ 0 & 4 & 0 & 2 \\ 0 & -3/2 & -1/2 & -4\end{array}\right)\rightarrow\left(\begin{array}{ccc|c}1 & 0 & 1/2 & -1 \\ 0 & 3/2 & 0 & 3 \\ 0 & -3/2 & -1/2 & -4\end{array}\right) \\ \\ \rightarrow\left(\begin{array}{ccc|c}1 & 0 & 1/2 & -1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2\end{array}\right)\rightarrow\left(\begin{array}{ccc|c}1 & 0 & 0 & -2 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2\end{array}\right) \end{gathered}$

So, the solution is:

$(-2,2,2)$