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4.8 Augmented Matrices and Systems

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4.8 Augmented Matrices and Systems 1. Cramer s Rule 1) Cramer s Rule Cramer s Rule is a method of solving systems even MORE quickly and easily than with ... – PowerPoint PPT presentation

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Title: 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
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