Answer
The matrix is,
$\left[ \begin{matrix}
1 \\
-1 \\
2 \\
-2 \\
0 \\
\end{matrix} \right]$
Work Step by Step
The augmented matrix for the provided system of equations is:
$\left[ \begin{matrix}
2 & -2 & 3 & -1 & 0 & 12 \\
1 & 2 & -1 & 2 & -1 & -7 \\
1 & 0 & 1 & 1 & -5 & 1 \\
-1 & 1 & -1 & -2 & -3 & 0 \\
1 & -1 & 0 & -1 & -1 & 4 \\
\end{matrix} \right]$
Follow the steps given below to solve the provided equations:
Step 1: Open the Ti-83 calculator and press the $\left[ 2\text{nd} \right]$ key then press $\left[ \text{MATRIX} \right]$ key.
Step 2: Press $\left[ 2\text{nd} \right]$ key, and ${{x}^{-1}}$ then press $\left[ \text{MATRIX} \right]$ key.
Use right arrow and select $\left[ \text{EDIT} \right]$. Enter $\left[ 1 \right]$ for matrix $\left[ \text{A} \right]$ then enter the order of the matrix then press $\left[ \text{ENTER} \right]$ key and enter the elements into the matrix.
Step 3: Press $\left[ 2\text{nd} \right]$ and $\left[ \text{MATRIX} \right]$ key then go to “MATH” and select “rref (“.
Step 4: Press $\left[ \text{ENTER} \right]$, then press $\left[ 2\text{nd} \right]$ key and 1, then press $\left[ \text{ENTER} \right]$ key.
The resulting matrix is:
$\left[ \begin{matrix}
1 & 0 & 0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 0 & -1 \\
0 & 0 & 1 & 0 & 0 & 2 \\
0 & 0 & 0 & 1 & 0 & -2 \\
0 & 0 & 0 & 0 & 1 & 0 \\
\end{matrix} \right]$
Hence, the solution is:
$\left[ \begin{matrix}
1 \\
-1 \\
2 \\
-2 \\
0 \\
\end{matrix} \right]$
The solution of the provided system is,
$\left[ \begin{matrix}
1 \\
-1 \\
2 \\
-2 \\
0 \\
\end{matrix} \right]$
