The mathematical matrix represents the rectangular massif of elements (for example, complex or real numbers). Each matrix has dimension which is designated by m*n where m is number of lines, n there is a number of columns. On crossing of lines and columns elements of the set set are located. Matrixes are designated by capital letters of A, B, C, D, etc., or A = (aij) where aij – an element on crossing of i – y lines and j – go a matrix column. The matrix is called square if its number of lines is equal to number of columns. Now we will enter a concept of determinant of a square matrix of n – go about.
Instruction
1. Let's consider a square matrix of A = (aij) of any n – go about. An aij element minor the matrix of A is called the determinant of an order of n-1 corresponding to a matrix of i received from a matrix by A deletion from it – y lines and j – go a column, i.e. lines and on which column the aij element is located. The minor is designated by letter M with coefficients: i – the line number, j is number of a column. The determinant of an order of n corresponding to a matrix of A is called the number designated by a symbol?. The determinant is calculated on the formula presented in the drawing where M - a minor to the a1j element.
2. Thus, if the matrix of A has the second order, i.e. n = 2, then the determinant corresponding to this matrix will be equal? = detA = a11a22 – a12a21
3. If the matrix of A has the third order, i.e. n = 3, then corresponding to this matrix determinant will be equal? = detA = a11a22a33? a11a23a32? a12a21a33 + a12a23a31 + a13a21a32? a13a22a31
4. Calculation of determinants of an order n> 3 it is possible to make a method of decrease in an order of determinant which is based on zeroing of everything, except one, determinant elements by means of properties of determinants.