Determinants and their Applications

Singular matrix

A square matrix with determinant zero is called a singular matrix.

1

$\cos \theta \cdot \cos \theta - (-\sin \theta) \cdot \sin \theta = \cos^2 \theta + \sin^2 \theta = 1$.

1

The minor of $a_{22}$ is the determinant obtained by deleting row 2 and column 2, which leaves the element 1.

(-1)^{i+j} × minor

The cofactor is $(-1)^{i+j}$ times the minor of the element.