Answer:
System of equations:
[tex]x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6[/tex]
Augmented matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]
Reduced Row Echelon matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]
Step-by-step explanation:
Convert the system into an augmented matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]
For notation, R_n is the new nth row and r_n the unchanged one.
1. Operations:
[tex]R_2=-2r_1+r_2\\R_3=-r_1+r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right][/tex]
2. Operations:
[tex]R_2=-\frac{1}{3}r_2[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right][/tex]
3. Operations:
[tex]R_3=r_2+r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right][/tex]
4. Operations:
[tex]R_3=\frac{1}{2}r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]
