Every square matrix is associated with a real number which is called the determinant of the square matrix. Let S be the set of all square matrices and R be the set of real numbers. Then the function f:S->R is called the determinant. The determinant of a matrix M is denoted by |M| or detM.
The determinant of a matrix has some properties. Usually the process of solving system of linear equations is more difficult if the number of variables exceeds 2. But these properties of determinants are most helpful in solving a system of equations.
a) The value of the determinant does not change if the rows and columns are interchanged.
b) If any two rows (or columns) of a determinant are interchanged then the sign of the determinant changes.
(Here, 2nd and 3rd rows are interchanged).
c) The value of a determinant with any two identical rows (or columns) is zero.
(Here, first and second rows are identical).
d) If each element of a row (or column) are multiplied by a scalar k then the value of the determinant thus obtained is equal to k times the actual determinant.
(Here the elements of the first row are multiplied by 2).
e) The value of a determinant is unchanged though a row (or column) is added to the corresponding elements of the multiplies of the other row (or column).
Replacing the second row with the sum of the second row with the corresponding elements of multiples of 2 of the first row, we get
f) If all the elements in a row (or column) of a determinant are zeroes then the value of the determinant is zero.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Pembroke visit: Tutoring in Pembroke .