103 - Linear equation variables constant term coefficients...

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1 Linear equation variables coefficients constant term System of linear equations ( m equations, n variables) two linear equations in two variables (two lines in R 2 ): no solution unique solution infinitely many solution Solution set: the set of all solutions. Inconsistent system of linear equations: solution set is empty. Equivalent systems of linear equations: having the same solution set. Elementary row operations for solving systems of linear equations: (Will be proved subsequently.) ( 2) × ( ( ) ) × ( 3) + + ⇔⇔ ( ) × ( 1/2) ( 3) × ( ( ) ) × 1 + +
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2 ( ) × ( 1/3) ( ) × 2 + The manipulations are on the coefficients and constant terms only, so the variables x 1 , x 2 , and x 3 need not be shown, and we represent the system of linear equations by the augmented matrix A x = b = [ A b ] on which we perform the manipulations. A : coefficient matrix Properties: 1. Every elementary row operations are reversible. For interchange operation it is obvious, for scaling operation multiply the inverse of the nonzero constant, and for row addition operation add the negative multiple of the row to the other row.
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103 - Linear equation variables constant term coefficients...

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