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