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When using Gaussian elimination to solve a system of linear equations , we can add a multiple of one equation to another and have an equivalent equation

In other words , If we have a system of three linear equations L1 , L2 and L3 we can multiply L1 by a nonzero multiple and add it to L2 to get an equivalent equation to L2

why is that valid ?

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    Proof is easy, show soloution of one system is also soloution of other. Have you tried it ?2012-09-23
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    You do not generally get an equation that is equivalent to $L_2$. The *system of equations*, however, is equivalent to the original system.2012-09-23
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    @Akram Please do not write comments as answers.2012-09-24

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