Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the...

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example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations 2 3 1 2 3 3 9 x y z x y z x y z 2009 PBLPathways

Transcript of Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the...

Page 1: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

example 1 Matrix Solution of Linear Systems

Chapter 7.2

Use matrix row operations to solve the system of equations

2 3 1

2 3

3 9

x y z

x y z

x y z

2009 PBLPathways

Page 2: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

Use matrix row operations to solve the system of equations

2 3 1

2 3

3 9

x y z

x y z

x y z

Page 3: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

Use matrix row operations to solve the system of equations

2 3 1

2 3

3 9

x y z

x y z

x y z

2 3

2 3 1

3 9

x y z

x y z

x y z

R1 R2

2 3 1 1

1 1 2 3

3 1 1 9

1 1 2 3

2 3 1 1

3 1 1 9

Page 4: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

Use matrix row operations to solve the system of equations

2 3 1

2 3

3 9

x y z

x y z

x y z

2 3

2 3 1

3 9

x y z

x y z

x y z

R1 R2

2 3 1 1

1 1 2 3

3 1 1 9

1 1 2 3

2 3 1 1

3 1 1 9

Page 5: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

Use matrix row operations to solve the system of equations

2 3 1

2 3

3 9

x y z

x y z

x y z

2 3

2 3 1

3 9

x y z

x y z

x y z

R1 R2

2 3 1 1

1 1 2 3

3 1 1 9

1 1 2 3

2 3 1 1

3 1 1 9

Page 6: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

2 2 4 6

2 3 1 1

0 1 3 5

Page 7: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

2 2 4 6

2 3 1 1

0 1 3 5

Page 8: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

2 2 4 6

2 3 1 1

0 1 3 5

Page 9: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 10: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 11: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 12: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 13: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 14: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 15: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

4 7 18

x y z

y z

y z

-1 R2 R2 1 1 2 3

0 1 3 5

0 4 7 18

-2 R1 + R2 R2-3 R1 + R3 R3

2 3

3 5

4 7 18

x y z

y z

y z

1 1 2 3

0 1 3 5

0 4 7 18

1 1 2 3

2 3 1 1

3 1 1 9

3 3 6 9

3 1 1 9

0 4 7 18

Page 16: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 17: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 18: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 19: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 20: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 21: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 22: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 23: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 24: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 25: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 26: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38

Page 27: Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

2009 PBLPathways

2 3

3 5

19 38

x y z

y z

z

-4 R2 + R3 R3

2 3

3 5

2

x y z

y z

z

R3 R3119

1 1 2 3

0 1 3 5

0 0 19 38

1 1 2 3

0 1 3 5

0 0 1 2

1 1 2 3

0 1 3 5

0 4 7 18

0 4 12 20

0 4 7 18

0 0 19 38