Quantitative Analysis for Management, 13/e

M5.2 Determinants, Cofactors, and Adjoints

There are other important concepts related to matrices. These include the determinant, cofactor, and adjoint of a matrix.

Determinants

A determinant is a value associated with a square matrix. As a mathematical tool, determinants are of value in helping to solve a series of simultaneous equations.

A 2-row by 2-column $\left(2\times 2\right)$ determinant can be expressed by enclosing vertical lines around the matrix, as shown here:

$$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$$

Similarly, a $3\times 3$ determinant is indicated as

$$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$$

One common procedure for finding the determinant of a $2\times 2$ or $3\times 3$ matrix is to draw its primary and secondary diagonals. In the case of a $2\times 2$ determinant, the value is found by multiplying the numbers on the primary diagonal and ...