Determinants

       
           

The determinants definition states that it is a value which is derived in the sense of square matrix. Determinants are calculated by the entries of a square matrix by specified arithmetic term. The Determinant is used to provide the important information, if it is the coefficient of the matrix of system of linear equation, or when we apply linear transformation of a vector space. When the value of the determinant is nonzero then the whole system has a unique solution and it is the first case, and while working with the second case the whole result is used to transform in the inverse operation.

In calculus mathematics the determinant is used to show the characteristic polynomial of a matrix. In the linear algebra the determinant is also used to calculate the Eigen value and Eigen vector.

Let (p) be the determinant of a matrix Q, then it will be concluded as

[ a b c]

[ d e f ]

[ g h i ]  is written as, and has the value  ( a e i ) + ( b f g ) + ( c d h ) - ( c e g ) – ( b d I ) – ( a f h ).

The value of determinants can be understood as:

Suppose we has a matrix Q = [ a  b ],

                                               [ c  d ]2x2  of order 2  X 2,

The entries a, b, c, d are real numbers then its determinant is defined as below

Q = [ a  b ],

       [ c  d ] = ad – bc.

Here we get to know that (ad – bc) is the area of the parallelogram. So it represents the scalar factor which makes us understand that it transforms the value of Q.

This is all about maths determinants.

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