A First Course in Linear Algebra · Problem PDM-M20

Eigenvalues — Robert Beezer

Mathematics — Linear Algebra · cofactor-matrix

Problem

Construct a

3 \times 3

nonsingular matrix and call it

A

. Then, for each entry of the matrix, compute the corresponding cofactor, and create a new

3 \times 3

matrix full of these cofactors by placing the cofactor of an entry in the same location as the entry it was based on. Once complete, call this matrix

C

. Compute

AC^t

. Any observations? Repeat with a new matrix, or perhaps with a

4 \times 4

matrix.