Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 3 x 1 + x 2 +9 - PowerPoint PPT Presentation

Solving a linear system  − 2 x 1 +2 x 2 +10 x 3 = 2  − 3 x 1 + x 2 +9 x 3 = 5 4 x 1 − 2 x 2 − 14 x 3 = − 6 

Solving a linear system  − 2 x 1 +2 x 2 +10 x 3 = 2 R 1 ← 1 2 R 1  − 3 x 1 + x 2 +9 x 3 = 5 − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 

Solving a linear system   − 2 x 1 +2 x 2 +10 x 3 = 2 − 5 x 3 = − 1 x 1 − x 2 R 1 ← 1 2 R 1   − 3 x 1 + x 2 +9 x 3 = 5 − 3 x 1 + x 2 +9 x 3 = 5 − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 4 x 1 − 2 x 2 − 14 x 3 = − 6  

Solving a linear system   − 2 x 1 +2 x 2 +10 x 3 = 2 − 5 x 3 = − 1 x 1 − x 2 R 1 ← 1 2 R 1   − 3 x 1 + x 2 +9 x 3 = 5 − 3 x 1 + x 2 +9 x 3 = 5 − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 4 x 1 − 2 x 2 − 14 x 3 = − 6       − 2 2 10 2 1 − 1 − 5 − 1 R 1 ← 1 2 R 1 − 3 1 9 5 − 3 1 9 5 − − − − − →     4 − 2 − 14 − 6 4 − 2 − 14 − 6

Solving a linear system  − 5 x 3 = − 1 x 1 − x 2  − 3 x 1 + x 2 +9 x 3 = 5 4 x 1 − 2 x 2 − 14 x 3 = − 6 

Solving a linear system  − 5 x 3 = − 1 x 1 − x 2  R 2 ← R 2 +3 R 1 − 3 x 1 + x 2 +9 x 3 = 5 − − − − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 

Solving a linear system   − 5 x 3 = − 1 − 5 x 3 = − 1 x 1 − x 2 x 1 − x 2   R 2 ← R 2 +3 R 1 − 3 x 1 + x 2 +9 x 3 = 5 − 2 x 2 − 6 x 3 = 2 − − − − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 4 x 1 − 2 x 2 − 14 x 3 = − 6  

Solving a linear system   − 5 x 3 = − 1 − 5 x 3 = − 1 x 1 − x 2 x 1 − x 2   R 2 ← R 2 +3 R 1 − 3 x 1 + x 2 +9 x 3 = 5 − 2 x 2 − 6 x 3 = 2 − − − − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 4 x 1 − 2 x 2 − 14 x 3 = − 6       1 − 1 − 5 − 1 1 − 1 − 5 − 1 R 2 ← R 2 +3 R 1 − 3 1 9 5 0 − 2 − 6 2 − − − − − − − − →     4 − 2 − 14 − 6 4 − 2 − 14 − 6

Solving a linear system   − 5 x 3 = − 1 x 1 − x 2 − 5 x 3 = − 1 x 1 − x 2   R 3 ← R 3 − 4 R 1 − 2 x 2 − 6 x 3 = 2 − 2 x 2 − 6 x 3 = 2 − − − − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 2 x 2 +6 x 3 = − 2  

Solving a linear system   − 5 x 3 = − 1 x 1 − x 2 − 5 x 3 = − 1 x 1 − x 2   R 3 ← R 3 − 4 R 1 − 2 x 2 − 6 x 3 = 2 − 2 x 2 − 6 x 3 = 2 − − − − − − − − → 4 x 1 − 2 x 2 − 14 x 3 = − 6 2 x 2 +6 x 3 = − 2       1 − 1 − 5 − 1 1 − 1 − 5 − 1 R 3 ← R 3 − 4 R 1 0 − 2 − 6 2 0 − 2 − 6 2 − − − − − − − − →     4 − 2 − 14 − 6 0 2 6 − 2

Solving a linear system   x 1 − x 2 − 5 x 3 = − 1 x 1 − x 2 − 5 x 3 = − 1   R 3 ← R 3 + R 2 − 2 x 2 − 6 x 3 = 2 − 2 x 2 − 6 x 3 = 2 − − − − − − − → 2 x 2 +6 x 3 = − 2 0 = 0  

Solving a linear system   x 1 − x 2 − 5 x 3 = − 1 x 1 − x 2 − 5 x 3 = − 1   R 3 ← R 3 + R 2 − 2 x 2 − 6 x 3 = 2 − 2 x 2 − 6 x 3 = 2 − − − − − − − → 2 x 2 +6 x 3 = − 2 0 = 0       1 − 1 − 5 − 1 1 − 1 − 5 − 1 R 3 ← R 3 + R 2 0 − 2 − 6 2 0 − 2 − 6 2 − − − − − − − →     0 2 6 − 2 0 0 0 0

Solving a linear system � x 1 − x 2 − 5 x 3 = − 1 � x 1 − x 2 − 5 x 3 = − 1 R 3 ←− 1 2 R 3 − − − − − − → − 2 x 2 − 6 x 3 = 2 +3 x 3 = − 1 x 2

Solving a linear system � x 1 − x 2 − 5 x 3 = − 1 � x 1 − x 2 − 5 x 3 = − 1 R 3 ←− 1 2 R 3 − − − − − − → − 2 x 2 − 6 x 3 = 2 +3 x 3 = − 1 x 2     1 − 1 − 5 − 1 1 − 1 − 5 − 1 R 3 ←− 1 2 R 3 0 − 2 − 6 2 0 1 3 − 1 − − − − − − →     0 0 0 0 0 0 0 0

Solving a linear system � x 1 − x 2 − 5 x 3 = − 1 � x 1 − x 2 − 5 x 3 = − 1 R 1 ← R 1 + R 2 − − − − − − − → +3 x 3 = − 1 +3 x 3 = − 1 x 2 x 2

Solving a linear system � x 1 − x 2 − 5 x 3 = − 1 � x 1 − x 2 − 5 x 3 = − 1 R 1 ← R 1 + R 2 − − − − − − − → +3 x 3 = − 1 +3 x 3 = − 1 x 2 x 2     1 − 1 − 5 − 1 1 0 − 2 − 2 R 1 ← R 1 + R 2 0 1 3 − 1 0 1 3 − 1 − − − − − − − →     0 0 0 0 0 0 0 0

Solving a linear system   1 0 − 2 − 2 0 1 3 − 1   0 0 0 0

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0 � x 1 = 2 x 3 − 2 = ⇒ x 2 = − 3 x 3 − 1   x 1 = x 2 ⇒   x 3

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0 � x 1 = 2 x 3 − 2 = ⇒ x 2 = − 3 x 3 − 1     2 t − 2 x 1  = = − 3 t − 1 x 2 ⇒    x 3 t

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0 � x 1 = 2 x 3 − 2 = ⇒ x 2 = − 3 x 3 − 1         2 t − 2 2 t − 2 x 1  =  = = − 3 t − 1 − 3 t  + − 1 x 2 ⇒      0 x 3 t t

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0 � x 1 = 2 x 3 − 2 = ⇒ x 2 = − 3 x 3 − 1             2 t − 2 2 t − 2 2 − 2 x 1  =  =  = = − 3 t − 1 − 3 t  + − 1 − 3  t + − 1 x 2 ⇒        0 1 0 x 3 t t

Solving a linear system   1 0 − 2 − 2 � x 1 − 2 x 3 = − 2 0 1 3 − 1 �   x 2 +3 x 3 = − 1 0 0 0 0 � x 1 = 2 x 3 − 2 = ⇒ x 2 = − 3 x 3 − 1             2 t − 2 2 t − 2 2 − 2 x 1  =  =  = = − 3 t − 1 − 3 t  + − 1 − 3  t + − 1 x 2 ⇒        0 1 0 x 3 t t (Parametric form)

Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 3 x 1 + x 2 +9 - PowerPoint PPT Presentation

Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 3 x 1 + x 2 +9 x 3 = 5 4 x 1 2 x 2 14 x 3 = 6 Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 R 1 1 2 R 1 3 x 1 + x 2 +9 x 3 = 5

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Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 3 x 1 + x 2 +9 - PowerPoint PPT Presentation

Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 3 x 1 + x 2 +9 x 3 = 5 4 x 1 2 x 2 14 x 3 = 6 Solving a linear system 2 x 1 +2 x 2 +10 x 3 = 2 R 1 1 2 R 1 3 x 1 + x 2 +9 x 3 = 5

Solving Linear System of Equations The Undo button for Linear Operations Matrix-vector

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Parametric Linear System Solving with Error Correction. Cleveland Waddell S YMBOLIC -N UMERIC C

Polynomial Linear System Solving with Errors by Simultaneous Polynomial Reconstruction of

Solving Systems Solving Systems by Graphing by Solving Systems by Substitution Graphing

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solving systems L. Olson Department of Computer Science University of Illinois at

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