Use Gauss-Jordan elimination to solve the system.
\[
\left\{\begin{array}{rlr}
x+z & =1 \\
5 x-y+z & = & -4 \\
x+y & = & 10
\end{array}\right.
\]

Answer

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Answer

\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -7 \\ 0 & 0 & 1 & 0 \end{bmatrix}

Steps

Step 1 ：\begin{bmatrix} 1 & 0 & 1 & 1 \\ 5 & -1 & 1 & -4 \\ 1 & 1 & 0 & 10 \end{bmatrix}

Step 2 ：\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0 & -1 & -4 & -9 \\ 0 & 1 & -1 & 9 \end{bmatrix}

Step 3 ：\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0 & 1 & 4 & 9 \\ 0 & 1 & -1 & 9 \end{bmatrix}

Step 4 ：\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0 & 1 & 4 & 9 \\ 0 & 0 & -5 & 0 \end{bmatrix}

Step 5 ：\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0 & 1 & 4 & 9 \\ 0 & 0 & 1 & 0 \end{bmatrix}

Step 6 ：\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -7 \\ 0 & 0 & 1 & 0 \end{bmatrix}