Quiz Gauss-Jordan Elimination / Homogeneous System. Math 2568 Spring 2018.

Question

x1+x2−x5x2+2x3+x4+3x5x1−x3+x4+x5=1=1=0

Solution

The augmented matrix of the system is

⎡⎣⎢⎢10111002−1011−131110⎤⎦⎥⎥..

We apply elementary row operations as follows.

⎡⎣⎢⎢10111002−1011−131110⎤⎦⎥⎥−→−−−R3−R1⎡⎣⎢⎢10011−102−1011−13211−1⎤⎦⎥⎥−→−−−R1−R2R3+R2⎡⎣⎢⎢100010−221−112−435010⎤⎦⎥⎥−→−−−−R1+2R3R2−2R3⎡⎣⎢⎢1000100013−326−75010⎤⎦⎥⎥.

Answer

x1x2x3=−3x4−6x5=3x4+7x5+1=−2x4−5x5$$$$