Determinant of a matrix is the polynomial from various works of its elements. One of ways of calculation of determinant is decomposition of a matrix on a column on additional minors (submatrixes).
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Instruction
1. It is known that the determinant of a matrix of the second order is calculated so: the work of elements of collateral diagonal is subtracted from the work of elements of the main diagonal. Therefore it is convenient to spread out a matrix to minors of the second order and then already to calculate determinants of these minors and also determinant of an initial matrix. In the drawing the formula for calculation of determinant of any matrix is presented. Using it, we will spread out a matrix at first to minors of the third order, and then each received minor on minors of the second order that will allow to calculate a determinant of matrixes easily.
2. Let's spread out on a formula an initial matrix to additional matrixes of size 3 on 3. Additional matrixes, or minors, are formed by deletion of an initial matrix of one line and one column. In a row polynomials such minors enter increased by that element of a matrix to which they are additional, the sign of a polynomial is defined by degree-1 which represents the sum of indexes of an element.
3. Now we display each of matrixes of the third order in the same way on matrixes of the second order. We find determinant of each such matrix and we will receive a number of polynomials from elements of an initial matrix, there are purely arithmetic calculations further.