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9 Systems of Equations and Inequalities > 9.2 Determinants and Cramer’s Rule
9.2 Determinants and Cramer’s Rule
Introduction If a linear system of equations has the same number of equations as it does variables, say two equations and two variables, then it may be possible to solve the system using determinants. If a11, a12, … represent real numbers, then the symbols
are called determinants of order 2 and order 3, respectively. Although a determinant can be any order n, n a positive integer, most of the elementary applications of determinants in calculus utilize second- and third-order determinants.
Determinant of Order 2 A determinant is a number. In the case of a determinant of order 2 we have the following definition.
DEFINITION 9.2.1 Determinant of Order 2
A determinant of order 2 is the number
EXAMPLE 1 Determinant of Order 2
