TABLE OF CONTENTS A square matrix of order n (an n n matrix)
possesses a uniquely defined scalar (a single number) which is designated as the determinant of A or merely the determinant
where the order of the determinant is the same as the order of the matrix from which it derives. Observe that only square matrices possess determinants, the use of vertical lines and not brackets to designate determinants and that the elements of the determinant are identical to the elements of the matrix
A determinant of the first order consists of a single element, a, and has, therefore, the value det A = a. A determinant of the second order contains four elements in a 2 2 square array with the value
A determinant of the third order is described in similar fashion. It is a 3 3 square array containing nine elements
One may deduce that a determinant of the n th order consists of a square array of n n elements, a ij, and that the total number of elements in an n th order determinant is n 2.
Although the concept of the determinant looks to be purely abstract, the determinant can be proved to be a very rational function which can be evaluated in a number of ways. Moreover, the value of the use of determinants in the taking of matrix inverses and in the solution of simultaneous,...
