lect1104RowOperations

# - MATH 17100 28446 Systems of Linear Equations and Elementary Row operations Given the system of m linear equations in n unknowns x1 x2 xn a11 x1

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MATH 17100 28446 11/04/2009 Systems of Linear Equations and Elementary Row operations Given the system of m linear equations in n unknowns 12 ,,, n xx x : 11 1 12 2 1 1 nn ax ax ax b + ++ = …………. . (1) 21 1 22 2 2 2 11 2 2 (2) () m m mn n m m + = + = .................. .................. we can recast them in matrix form : = Ax b . Here A is the mn × coefficient matrix 11 12 1 21 22 2 n n m m mn aa a a a     , x is the 1 n × matrix 1 2 n x x x , the components being the unknowns of the system of equations to be solved for, b is the 1 m × matrix 1 2 m b b b . The augmented matrix [ A | b] is the ( 1) ×+ matrix that has the column matrix b appended to the right of A : [A | b] = 11 12 1 1 21 22 2 2 n n m m mn m a a ab    

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Each row in the augmented matrix corresponds to an equation in the given system of equations. The usual procedure followed in the solution procedure called the Method of Elimination consists of the three types of operations: (1) Interchange of two equations (2) Multiply ing an equation
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## This note was uploaded on 11/04/2010 for the course MATH 17100 taught by Professor Kitchens during the Spring '10 term at IUPUI.

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- MATH 17100 28446 Systems of Linear Equations and Elementary Row operations Given the system of m linear equations in n unknowns x1 x2 xn a11 x1

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