1. 9-5 Higher Order Determinants
Cramer’s Rule and 3 by 3’s

2. How to Evaluate a 3 by 3 Determinant
ceg
afh
bdi
aei
bfg
cdh + + – – –

3. Example
1. Evaluate

4. Cramer’s Rule
It will look scary at first, but it is the SAME EXACT CONCEPT as a 2 by 2 situation.
That is, the denominator of each solution is the determinant of the coefficients.
The numerator is the coefficient determinant with the appropriate column replaced by the solutions. That is, the x column replaced when solving for x, the y column when solving for y and the z column when solving for z.

5. Hint: if you can find x and y, just sub in to find z

6. Examples 2. 3.
Uhoh…what happens when the denominator equals zero?