Answer:
Step-by-step explanation:
Consider the 3x3 matrices in row echelon form:
[tex]\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&0\end{array}\right][/tex]
and
[tex]\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&1\end{array}\right][/tex]
a) The augmented matrix
[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&0&2\end{array}\right][/tex]
corresponds to an inconsistent system.
b) The augmented matrix
[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&0&0\end{array}\right][/tex]
corresponds to a consistent system with infinite solutions.
(c) The augmented matrix
[tex]\left[\begin{array}{ccc|c}1&2&0&1\\0&1&2&1\\0&0&1&1\end{array}\right][/tex]
corresponds to a consistent system with infinite solutions.
