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**Unformatted text preview: **NOTES ON SECTION 1 . 1 MA265, SECTIONS 41, 52 Overview: this section introduces systems of equations, summarizes the solution process, and describes the possible solution sets. Key words Linear equation Consistent System Unique Solution Solution of a linear equation Homogeneous System No Solution Linear System Infinitely many solutions Unknowns Nontrivial solutions Row operation Inconsistent System Equivalent systems Method of elimination Summary: Given variables ( unknowns ) x 1 ,x 2 ,...,x n coefficients a 1 ,...,a n , b Definition 1. A linear equation is an equation a 1 x 1 + a 2 x 2 + + a n x n = b Definition 2. A linear system of m linear equation in n unknowns is a system of linear equations a 11 x 1 + a 12 x 2 + ... + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + ... + a 2 n x n = b 2 . . . = . . . a m 1 x 1 + a m 2 x 2 + ... + a mn x n = b m A solution is an assignment of values to the variables x 1 ,...,x n such that each and every equation in...

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