Two Methods of Evaluating Determinants

[msu_math]

In linear algebra, the determinant is a value (scalar quantity) associated with a square matrix. The determinant of a square matrix A is usually denoted by |A|. For a square matrix A[a_ij] of order 2, |A| is defined to equal the value a₁₁a₂₂ - a₂₁a₁₂. Determinant of higher order matrices are evaluated recursively by combining the determinants of lower order matrices in a specific arithmetic manner.

Two frequently used methods for evaluating determinants:

1. Co-factor Expansion Method:   http://oase.daffodilvarsity.edu.bd/MatDet_input.php

2. Row Reduction Method:   http://oase.daffodilvarsity.edu.bd/MatDetReduc_input.php

[msu_math]

Applications of Determinant: The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector space: in the first case the system has a unique solution if and only if the determinant is nonzero, while in the second case that same condition means that the transformation has an inverse operation.

[proteeti]

necessary!!

[Anuz]

Thanks

[Tofazzal.ns]

Thanks for sharing.