4.8 Augmented Matrices and Systems

1
4.8 Augmented Matrices and Systems

• 1. Cramers Rule

2
1) Cramers Rule

• Cramers Rule is a method of solving systems even
  MORE quickly and easily than with matrices and
  inverses.

3
1) Cramers Rule
System
Coefficients
4
1) Cramers Rule
y- component of the solution
x- component of the solution
System
Coefficients
5
1) Cramers Rule
y- component of the solution
x- component of the solution
System
Coefficients
y- stays the same
6
1) Cramers Rule
y- component of the solution
x- component of the solution
System
Coefficients
x- stays the same
7
1) Cramers Rule
y- component of the solution
x- component of the solution
System
Coefficients
The solution of the system is
8
1) Cramers Rule
y- component of the solution
x- component of the solution
System
Coefficients
The solution of the system is
Cramers Rule
9
1) Cramers Rule

• Example 1
• Use Cramers Rule to solve the system

10
1) Cramers Rule

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

11
1) Cramers Rule

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

12
1) Cramers Rule

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

13
1) Cramers Rule

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

14
1) Cramers Rule

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

15
1) Cramers Rule

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

16
1) Cramers Rule

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

17
1) Cramers Rule

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

18
1) Cramers Rule

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

19
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).
20
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

21
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

22
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

23
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

24
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

25
1) Cramers Rule

• Example 2
• Use Cramers Rule to solve the system

The solution is (1, 2).
26
1) Cramers Rule

• LS/RS Check
• (x, y) (1, 2)

27
1) Cramers Rule

• LS/RS Check
• (x, y) (1, 2)

28
Homework

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