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4.8 Augmented Matrices and Systems

- 1. Cramers Rule

1) Cramers Rule

- Cramers Rule is a method of solving systems even

MORE quickly and easily than with matrices and

inverses.

1) Cramers Rule

System

Coefficients

1) Cramers Rule

y- component of the solution

x- component of the solution

System

Coefficients

1) Cramers Rule

y- component of the solution

x- component of the solution

System

Coefficients

y- stays the same

1) Cramers Rule

y- component of the solution

x- component of the solution

System

Coefficients

x- stays the same

1) Cramers Rule

y- component of the solution

x- component of the solution

System

Coefficients

The solution of the system is

1) Cramers Rule

y- component of the solution

x- component of the solution

System

Coefficients

The solution of the system is

Cramers Rule

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 1 Evaluate three determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 1 Evaluate three determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 1 Evaluate three determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 1 Evaluate three determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

1) Cramers Rule

- Example 1
- Use Cramers Rule to solve the system
- Step 2 Find x- and y- using the determinants.

The solution is (4, 1).

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

1) Cramers Rule

- Example 2
- Use Cramers Rule to solve the system

The solution is (1, 2).

1) Cramers Rule

- LS/RS Check
- (x, y) (1, 2)

1) Cramers Rule

- LS/RS Check
- (x, y) (1, 2)

Homework

- p.224 1-3, 24, 25, 32
- TEST Wednesday Nov 25
- Chapter 4 Matrices