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Unformatted text preview: CHAPTER 1. INTRODUCTION TO VECTORS 59 2.3.2 Adding a multiple of one equation to another The operation of adding a multiple of one equation to another does not change the solution set of the system of equations. For example, consider the system of equations a1s1+---+ansn =6 (1) fl1$1+“'+fln$n =3 If we add A times equation (1) to equation (2), we obtain the system a1s1+---+ansn 2%) (2) (osl + Aaflsl + - — - + (can + Aan)$n = 5 + Ab Proposition 1. The solution of the system (1) is the same as the solution of the system (2). 3'1 Proof. Let x = f be a solution of system (1) Then we have 37% ...
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