Answer:
x = 1, y=2, z=0, w=3
Step-by-step explanation:
The following system of linear equations is given:
[tex]x + y + z + w = 6 \\2x + 3y - w = 5 \\-3x + 4y + z + 2w = 11\\ x + 2y - z + w = 8[/tex]
Setting up a matrix to solve the system:
[tex]\left[\begin{array}{ccccc}1&1&1&1&|6\\2&3&0&-1&|5\\-3&4&1&2&|11\\1&2&-1&1&|8\end{array}\right]\\[/tex]
Applying the Gauss-Jordan elimination method:
[tex]\left[\begin{array}{ccccc}1&1&1&1&|6\\0&1&-2&-3&|-7\\0&7&4&5&|29\\0&1&-2&0&|2\end{array}\right] \\\left[\begin{array}{ccccc}1&1&1&1&|6\\0&1&-2&-3&|-7\\0&0&18&26&|78\\0&0&0&3&|9\end{array}\right] \\\\\left[\begin{array}{ccccc}1&0&0&0&|1\\0&1&0&0&|2\\0&0&1&0&|0\\0&0&0&1&|3\end{array}\right] \\[/tex]
Therefore, x = 1, y=2, z=0, w=3.
