How to consider determinant in a matrix

Matrix determinant - one of the most important concepts of linear algebra. The determinant of a matrix is a polynomial from elements of a square matrix. For finding of determinant there is the general rule for square matrixes of any order and also the simplified rules for special cases of square matrixes of the first, second and third orders.

It is required to you

• Square matrix of n-go of an order

Instruction

1. Let the square matrix have the first order, that is consists one only a11 element. Then a11 element will be determinant of such matrix.

2. Now let the square matrix has the second order, that is is a matrix 2x2. a11, a12 are elements of the first line of this matrix, and a21 and a22 - elements of the second line. The determinant of such matrix can be found by the rule which it is possible to call "cross-wise". The determinant of a matrix of A is equal |And| = a11*a22-a12*a21.

3. In square about it is possible to use "the rule of a triangle". This rule offers the "geometrical" scheme of calculation of determinant of such matrix, simple for storing. The rule is represented in the drawing. As a result |And| = a11*a22*a33+a12*a23*a31+a13*a21*a32-a11*a23*a32-a12*a21*a33-a13*a22*a31.

4. Generally for a square matrix of n-go of an order the determinant is set on a recursive formula: M with indexes is an additional minor of this matrix. A minor of a square matrix of an order of n M with indexes from i1 to ik above and indexes from j1 to jk below where k <=n, is a determinant of a matrix which turns out from initial deletion of i1...ik of lines and j1...jk of columns.