Every square matrix has a special quantity associated with it, called its determinant. The determinant is important because we will soon see that it gives us another way to solve a set of equations.
We indicate or denote the determinant of a square matrix either by writing det before the matrix, or by a symbol consisting of the elements of the matrix enclosed between vertical bars. Thus
The words element, row, column, principal and secondary diagonal for a determinant have the same meaning as for a square matrix.
In the determinant
each of the numbers 2, 5, 6, and 1 is called an element. There are two rows, the first row containing the elements 2 and 5, and the second row having the elements 6 and 1. There are also two columns, the first with elements 2 and 6, and the second with elements 5 and 1. The elements along the principal diagonal are 2 and 1, and along the secondary diagonal they are 5 and 6.
We find the value of a second order determinant by applying the following rule:
The value of a second-order determinant is equal to the product of the elements on the principal diagonal, minus the product of the elements on the secondary diagonal.
The value of the determinant ...