We perform Gaussian elimination to compute the reduced row echelon form of the augmented matrix:
Thus x 1 = 50 , x 2 = 250 , x 3 = 300. {\textstyle \color {blue}x_{1}=50,x_{2}=250,x_{3}=300.}
![{\displaystyle {\begin{aligned}\left[{\begin{array}{ccc|c}1&1&1&600\\-1&1&0&200\\1&1&-1&0\end{array}}\right]&\xrightarrow {R_{3}-R_{1}} \left[{\begin{array}{ccc|c}1&1&1&600\\-1&1&0&200\\0&0&-2&-600\end{array}}\right]&\xrightarrow {R_{2}+R_{1}} \left[{\begin{array}{ccc|c}1&1&1&600\\0&2&1&800\\0&0&-2&-600\end{array}}\right]&\xrightarrow {{\frac {R_{2}}{2}},-{\frac {R_{3}}{2}}} \left[{\begin{array}{ccc|c}1&1&1&600\\0&1&1/2&400\\0&0&1&300\end{array}}\right]\\&\xrightarrow {R_{1}-R_{2}} \left[{\begin{array}{ccc|c}1&0&1/2&200\\0&1&1/2&400\\0&0&1&300\end{array}}\right]&\xrightarrow {R_{2}-{\frac {1}{2}}R_{3}} \left[{\begin{array}{ccc|c}1&0&1/2&200\\0&1&0&250\\0&0&1&300\end{array}}\right]&\xrightarrow {R_{1}-{\frac {1}{2}}R_{3}} \left[{\begin{array}{ccc|c}1&0&0&50\\0&1&0&250\\0&0&1&300\end{array}}\right].\end{aligned}}}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/fda571c0843add682d05a449076ee864d04b7377)
