Numerical Solutions of Linear Systems of Equations
Numerical Solutions of Linear Systems of Equations
Numerical Solutions of Linear Systems of Equations
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EE 216 Class NotesGAUSS ELIMINATIONThe operations in the Gauss elimination are called elementary operations.Elementary operations for equations are:(I)(II)(III)Interchange <strong>of</strong> two equations.Multiplication <strong>of</strong> an equation by a nonzero constant.Addition <strong>of</strong> a constant multiple <strong>of</strong> one equation to another equation.Let us consider the set <strong>of</strong> linearly independent equations.2x - 4y + 5z = 36 … … (1)- 3x + 5y + 7z = 7 … … (2)5x + 3y - 8z = - 31 … … (3)Augmented matrix for the set is:⎛⎜⎜⎜⎝2− 35− 45357− 836 ⎞7− 31⎟⎟⎟⎠Step 1Eliminate x from the 2 nd and 3 rd equation.3R ′ +22→ R1R25R ′ → − +23R1R3Pages 3 <strong>of</strong> 21
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