College Algebra 9th txtbk

488 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
Formula (1) is easily remembered if you notice that the expression on the right is the
product of the elements on the principal diagonal, from upper left to lower right, minus the
product of the elements on the secondary diagonal, from lower left to upper right.
EXAMPLE 1 Evaluating a Second-Order Determinant
1 2
Find `
3 4 ` .
SOLUTIONS
1 2
det (A) `
3 4 `
(1)(4) (3)(2)
4 (6)
10
MATCHED PROBLEM 1
Find
3 5
`
4 2 ` .
ZZZ CAUTION ZZZ
Remember that A c 3 5
3 5
is a matrix, but ` represents a real number,
4 2 d
4 2 `
3 5
the determinant of A. We will often refer to ` as a determinant, and refer to
4 2 `
the process of finding the real number it represents as “evaluating the determinant.”
Technology Connections
Most graphing calculators have a command to calculate determinants.
On the TI-84, it is on the MATRIX-MATH menu.
In Figure 1, the determinant from Example 1 is calculated.
Z Figure 1
Z Evaluating Third-Order Determinants
Given the matrix
A C
a 11 a 12 a 13
a 21 a 22 a 23
a 31 a 32 a 33
S,
the third-order determinant of A is
a 11 a 12 a 13
det (A) † a 21 a 22 a 23 † a 11 a 22 a 33 a 11 a 32 a 23 a 21 a 32 a 13 a 21 a 12 a 33 (2)
a 31 a 32 a 33 a 31 a 12 a 23 a 31 a 22 a 13