Determinants by Cofactor Expansion Worksheet with Answer Key

What's on the worksheet

1. Let A = \begin{bmatrix} 3 & 2 & 0 \\ 4 & 5 & 4 \\ -3 & 0 & 2 \end{bmatrix}.
2. Find M for the matrix below.
4. For a number k, let K = \begin{bmatrix} 1 & k & 0 & 2 \\ 0 & 0 & 3 & 1 \\ 2 & 0 & 1 & k \\ 1 & 1 & 3 & 3 \end{bmatrix}.
5. Find Q for Q = \begin{bmatrix} 3 & 1 & 0 & 2 & 0 \\ 1 & 0 & 2 & 4 & 1 \\ 0 & 2 & 0 & 1 & 0 \\ 2 & 0 & 0 & 3 & 1 \\ 0 & 1 & -1 & 0 & 2 \end{bmatrix}…
6. Full cofactor expansion of an n × n matrix with no zero entries forms n! products, while row reduction to triangular form needs about 13n³…
7. For n ≥ 1, let D_n be the determinant of the n × n matrix with 3 in every diagonal position, 1 in every position just above or just below the…