Determinants and Singular/Non-Singular Matrices

Determinants

Example:

Find $\left|A\right|$ ,when $\mathbf{A} = \left[ \begin{array}{ll}5 & 6\\ 2 & 3 \end{array} \right]$

The theory of determinants is attributed to a German, Gottfried Wilhelm Leibniz. His work expanded upon the earlier work of Japanese mathematician Seki Kowa.

Key Fact:

Every square matrix has a determinant either zero or nonzero.

Determinants can be represented by $\mathbf{D}_{1}, \mathbf{D}_{2}, \mathbf{D}_{3}, \ldots$

The determinant of a matrix is not a matrix rather it is a number.

While writing determinant of a matrix, the elements of the matrix should be written inside the vertical bars instead of brackets used for matrices.

Example: Evaluate the determinants