ABSTRACT
A second order determinant involves four elements a , b, c and d which may
either be numbers (real or complex) or functions, and it is displayed by writing them as follows:
a b
c d
:
The value of this second order determinant is defined to be
a b
c d
adbc:
Thus, by way of example, we have
3 2 4 5
35(2)4 23,
1 i 1 2 2 i
(1 i)(2 i)12 1 i,
and
x1 3 2 x2
(x1)(x2)23 x2x8:
More generally, an nth order determinant involves n2 elements arranged in
n rows and n columns. The order of the determinant is the number of ele-
ments (entries) in a row on a column. Equivalently, the order of a determi-
nant is the number of elements in the diagonal line drawn from top left to
bottom right in the determinant; this is called the leading diagonal. We use
the convention that the symbol aij represents the element in a determinant
which is located in the ith row and the jth column. Thus a32 represents the element in row 3 and column 2, while a14 represents the element in row 1 and
column 4. This convention is illustrated in the following diagram:
11 12 1n a21 a22 . . . a2n
an1 an2 . . . ann
,
with the elements a11, a22, . . . , ann comprising the leading diagonal.