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# lec1_1 - NOTES ON SECTION 1 1 MA265 Overview this section...

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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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## This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue.

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lec1_1 - NOTES ON SECTION 1 1 MA265 Overview this section...

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