Exercise12

Consider the matrices

\begin{equation*} \begin{aligned} A = \left[\begin{array}{rr} 0 \amp 1 \\ 1 \amp 0 \\ \end{array}\right], \qquad \amp B = \left[\begin{array}{rrr} 0 \amp 1 \amp 0 \\ 1 \amp 0 \amp 1 \\ 0 \amp 1 \amp 0 \\ \end{array}\right], \\ \\ C = \left[\begin{array}{rrrr} 0 \amp 1 \amp 0 \amp 0 \\ 1 \amp 0 \amp 1 \amp 0 \\ 0 \amp 1 \amp 0 \amp 1 \\ 0 \amp 0 \amp 1 \amp 0 \\ \end{array}\right], \qquad \amp D = \left[\begin{array}{rrrrr} 0 \amp 1 \amp 0 \amp 0 \amp 0 \\ 1 \amp 0 \amp 1 \amp 0 \amp 0 \\ 0 \amp 1 \amp 0 \amp 1 \amp 0 \\ 0 \amp 0 \amp 1 \amp 0 \amp 1 \\ 0 \amp 0 \amp 0 \amp 1 \amp 0 \\ \end{array}\right] \end{aligned} \end{equation*}
1. Use row (and/or column) operations to find the determinants of these matrices.

2. Write the $$6\times6$$ and $$7\times7$$ matrices that follow in this pattern and state their determinants based on what you have seen.

in-context