Exercise5

Consider the system of equations described by the following augmented matrix.

\begin{equation*} \left[ \begin{array}{ccc|c} 1 \amp 2 \amp 3 \amp 1 \\ 4 \amp 5 \amp 6 \amp 4 \\ a \amp b \amp c \amp 9 \\ \end{array} \right] \text{.} \end{equation*}
  1. Find a choice for the parameters \(a\text{,}\) \(b\text{,}\) and \(c\) that causes the linear system to be inconsistent. Explain why your choice has this property.

  2. Find a choice for the parameters \(a\text{,}\) \(b\text{,}\) 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 \(a\text{,}\) \(b\text{,}\) and \(c\) that causes the linear system to have infinitely many solutions. Explain why your choice has this property.

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