Determinant of Order 2 A determinant of order 2 is a scalar value associated with a 2x2 matrix. It can be calculated using determinants of the submatrices c...
Determinant of Order 2
A determinant of order 2 is a scalar value associated with a 2x2 matrix. It can be calculated using determinants of the submatrices created by deleting the rows and columns corresponding to the rows and columns of the original matrix.
Properties of Determinants of Order 2
The determinant of a diagonal matrix (with all elements being zero) is zero.
The determinant of a matrix with positive and negative elements is negative.
The determinant of an orthogonal matrix (with rows and columns interchanged) is the negative of the determinant of the original matrix.
The determinant of a matrix is equal to the product of the determinants of its rows.
Determinant of Order 3
A determinant of order 3 is a scalar value associated with a 3x3 matrix. It can be calculated using determinants of submatrices created by deleting rows and columns corresponding to the rows and columns of the original matrix.
Properties of Determinants of Order 3
The determinant of an identity matrix (with all elements being 1) is 1.
The determinant of a matrix with positive and negative elements is negative.
The determinant of a symmetric matrix (with elements symmetric across the diagonal) is positive.
The determinant of a matrix is equal to the product of the determinants of its diagonal submatrices.
Examples
Determinant of Order 2:
| a b |
| c d |
det = ad - bc
Determinant of Order 3:
| a b c |
| d e f |
| g h i |
det = ai - bc + cd - ef + fg - gi