Exercise11

Consider the matrices

\begin{equation*} A = \left[\begin{array}{rrrr} 0 \amp 1 \amp 0 \amp 0 \\ 0 \amp 0 \amp 1 \amp 0 \\ 0 \amp 0 \amp 0 \amp 1 \\ 1 \amp 0 \amp 0 \amp 0 \\ \end{array}\right], B = \left[\begin{array}{rrrr} 0 \amp 1 \amp 0 \amp 0 \\ 1 \amp 0 \amp 0 \amp 0 \\ 0 \amp 0 \amp 0 \amp 1 \\ 0 \amp 0 \amp 1 \amp 0 \\ \end{array}\right], C = \left[\begin{array}{rrrr} 0 \amp 0 \amp 0 \amp a \\ 0 \amp 0 \amp b \amp 0 \\ 0 \amp c \amp 0 \amp 0 \\ d \amp 0 \amp 0 \amp 0 \\ \end{array}\right] \text{.} \end{equation*}

Use row operations to find the determinants of these matrices.

in-context