Exercise 7

Consider the linear system described by the following augmented matrix. $$\left[ \begin{array}{ccc|c} 1 & 2 & 3 & 1 \\ 4 & 5 & 6 & 4 \\ a & b & c & 9 \\ \end{array} \right]$$.

1. Find a choice for the parameters $a$, $b$, and $c$ that causes the linear system to be inconsistent. Explain why your choice has this property.

2. Find a choice for the parameters $a$, $b$, and $c$ that causes the linear system to have a unique solution. Explain why your choice has this property.

3. Find a choice for the parameters $a$, $b$, and $c$ that causes the linear system to have infinitely many solutions. Explain why your choice has this property.