1. Lesson 13-3: Determinants & Cramer’s Rule
Objective:
Students will:
Evaluate determinants and
Solve systems using Cramer’s Rule

2. All square (2 x 2, 3 x 3,…) matrices have a determinant
2 x 2 determinant:
Difference of products from diagonals (main diagonal 1st)
Notation | |
Example 1
Solution:-8

3. Cramer’s Rule (cont’d) then…
so…
and
if needed

4. Cramer’s Rule
Uses determinants to solve systems
System: 3x – 2y = -9
x + 2y = 5
D = determinant of coefficient matrix
Dx = determinant of matrix with constants in place of x coefficients
Dy = determinant of matrix with constants in place of y coefficients

5. Example 2 Solve Using Cramer’s Rule
4x + 3y = 1
2x + y = 5 D=
Dx=
Dy=
Solution is (7, -9)

6. 3 x 3 Determinant: D = a1 ● (b2c3- b3c2) - a2 ● (b1c3- b3c1) + a3 ●

7. Solving 3-variable systems: Determinants will be 3 x 3’s
Example x - y + 2z = 1
x – y + 2z = 3
-2x + 3y + z = 3 D=
Dx=
Dy=
Dz=
Solution: ( )