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**Unformatted text preview: **Systems of Linear Equations Linear Algebra and its Applications David C. Lay Winter 2008 p. 1/15 Method A linear equation in the variables x 1 , x 2 , . . . , x n is an equation of the form a 1 x 1 + a 2 x 2 + . . . + a n x n = b where the value b and coefficients a 1 , a 2 , . . . a n are real or complex numbers. Examples: 3 x 1 + 2 x 2- 5 x 3 = 10 ix 1- (3 + i ) x 2 =- 7 x 3 + 2 x 4 Winter 2008 p. 2/15 When we have a collection of one or more linear equations involving the same variables it is called a system of linear equations or a linear system . Examples: 2 x 1- x 2 =- 3 x 1 + x 2 = 0 or x 1- x 2 + x 3 = 0 2 x 1 + x 2 =- 1 4 x 2- x 3 = 1 Winter 2008 p. 3/15 When presented with a linear system the objective is to find a solution . A solution is a set of numbers ( c 1 , c 2 , . . . , c n ) such that, when plugged into the linear system, c 1 = x 1 , c 2 = x 2 , . . . , c n = x n , we get a true statement....

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