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Educational => Mathematics => Basic Maths => Topic started by: msu_math on November 14, 2012, 12:26:01 PM

Title: Two Methods of Evaluating Determinants
Post by: msu_math on November 14, 2012, 12:26:01 PM

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 (http://oase.daffodilvarsity.edu.bd/MatDet_input.php)

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

Title: Re: Two methods of evaluating determinants
Post by: msu_math on November 14, 2012, 12:27:19 PM

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.

Title: Re: Two Methods of Evaluating Determinants
Post by: proteeti on March 28, 2014, 10:50:20 PM

necessary!!

Title: Re: Two Methods of Evaluating Determinants
Post by: Anuz on November 14, 2016, 01:56:09 PM

Thanks

Title: Re: Two Methods of Evaluating Determinants
Post by: Tofazzal.ns on March 15, 2017, 11:41:33 PM

Thanks for sharing.