Determinant or the determinant of a matrix is the some number calculated on the special formulas made of combinations of her members.
Instruction
1. At once we will tell that the determinant can be calculated only for a square matrix. We will count determinant of a matrix as follows. It will be the sum of the coefficients standing in the first line, we will increase each of which by determinant of the matrix received from initial by deletion of a column and line in which costs the multiplied coefficient. Signs at these factors will alternate (at the first will be ""+", at the second will be "" -"", etc.). Let's note that this formula is right for elements of any lines - optional to take the first, just it is more convenient because of presentation.
2. There is also the second way. There is a certain algorithm of calculation. At first we will enter a concept of the main diagonal of a matrix - it is the elements standing on diagonal since a11 and finishing and (nn) (that is from the left top corner in the right lower). So, we will return to an algorithm. For a matrix from one element the determinant will be equal to value of this element. For a matrix 2х2 it will be the difference of works of the elements standing on the main and collateral diagonal (by analogy, collateral diagonal goes from the right top corner to the left lower). For a matrix 3х3 it will be act this way: the first two columns are signed to the right of the third once again. The matrix 3х5 turns out kind of. Kind of, it is just reception. Further works of elements on the turned-out three main diagonals and three collateral are summarized. These sums are subtracted. The received number will also be matrix determinant. On the picture other option of calculation is represented by the same method, just here we do without dopisyvaniye, and simply we multiply elements and we subtract the sums of works on the specified scheme.
3. For a matrix 4x4, 5x5, etc. the same such rule will be carried out, but there are difficulties in connection with a large number of rooms and peremnozheny / additions which should be executed so the risk increases to make a mistake. Therefore in such cases it is more favorable to use the first method. Let's note that the determinant of a single matrix is equal to unit what it is easy to make sure of.