Page 101 - A Course in Linear Algebra with Applications

3.3: Determinants and Inverses of Matrices 85

The reader should note that Cramer's Rule can only be
used when the linear system has the special form indicated.

Example 3.3.4
Solve the following linear system using Cramer's Rule.

X\ - X 2 - x 3 = 4
Xi + 2x 2 -x 3 = 2
2x ± = 1

Here

1 - 1 '4
A = 1 2 and B =
2 0 : ! )

Thus det(A) = 9, and Cramer's Rule gives the solution

4 - 1 -1
x x = 1/9 2 2 - 1 = 13/9,
1 0 1

1 4 - 1
x 2 = 1/9 1 2 - 1 = - 2 / 3 ,
2 1 1

1 - 1 4
= 1/9 1 2 2 = -17/9.
x 3
2 0 1

Exercises 3.3

1. For the matrices

2 5
A = and B =
4 7