# Determinant

Determinant

Determinant of Matrix

Determinant is a scalar value calculated from a square matrix. Determinant encodes certain properties of linear transformation described by the matrix.

Only square matrices have determinants. The number of rows or columns of the square matrix is called the Dimension or Order of the Matrix

Evaluation of Determinant of Matrix

One Dimension Matrix : For one dimension matrix [A], the Determinant is the scalar value A

Two Dimension Matrix

Evaluation of Determinant of 2 dimension Matrix – Example 1 : Evaluate

Three Dimension Matrix

Three Dimension Matrix – Steps of Computation

The 3 components may be computed in following steps:

Determinant Component Sign

Evaluation of Determinant of 3 dimension Matrix – Example 1

Properties of Determinants

1. The value of the Determinant remains unchanged if its rows and columns are interchanged.

2. If any two rows or columns of a Determinant are interchanged, then sign of determinant changes.

3. If any two rows (or columns) of a Determinant are identical (all corresponding elements are same), then value of Determinant is zero.

4. If each element of a row (or a column) of a determinant is multiplied by a constant k, then its value gets multiplied by k.

5. If some or all elements of a row or column of a determinant are expressed as sum of two (or more) terms, then the determinant can be expressed as sum of two (or more) determinants.