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Math Help - matrices equation solution 71

  1. #1
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    matrices equation solution 71

    if Ax=Bx then for every x vector in R^n then A=B

    is it true?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    True. If A\neq B then A-B=(c_{ij})\neq 0 so, there exists c_{kl}\neq 0. Choose an adequate x_0 such that (A-B)x_0\neq 0 or equivalently Ax_0\neq Bx_0.

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