Explain why the matrix \(C= \left[\begin{array}{cccc} 1 & 1 & 3 & -2 \\ 1 & 2 & 6 & -7 \\ -2 & -1 & -2 & -4 \\ -3 & -2 & -8 & 8 \end{array}\right] \) is or is not invertible.
Answer:
\[\operatorname{RREF} \left[\begin{array}{cccc} 1 & 1 & 3 & -2 \\ 1 & 2 & 6 & -7 \\ -2 & -1 & -2 & -4 \\ -3 & -2 & -8 & 8 \end{array}\right] = \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right] \]
\(C\) is invertible.