As we have already seen, square matrix is one that has the same number of rows and columns (ie is of type n x n). Every square matrix is associated with a number which we call determinant.
Among the various applications of determinants in mathematics, we have:
solving some types of systems of linear equations;
calculating the area of a triangle situated in the Cartesian plane, when the coordinates of its vertices are known;
1st order determinant
Given a 1st order square matrix M = a11, its determinant is the real number to11:
det M = la11I = a11
Note: We represent the determinant of a matrix between two vertical bars, which do not have the meaning of modulus. For example:
M = 5 det M = 5 or | 5 | = 5
M = -3 det M = -3 or | -3 | = -3
2nd order determinant
Given the matrix , order 2, by definition the determinant associated with M, 2nd order, is given by:
Therefore, the determinant of an array of order 2 is given by the difference between the product of the main diagonal elements and the product of the secondary diagonal elements. See the following example.
Next: Minor Complement