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In solving system of linear equation $Ax = b$ by $LU$ factorization why we take diagonal elements of lower triangular matrix $L$ or upper triangular matrix $U$ as $1$ only. I understand that to get the unique solution by $LU$ factorization we have to fix either diagonal elements of $L$ or of diagonal elements of $U$. Can't I take $2$ as the fix diagonal elements?

Thanks for the kind help.

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    @Moo Thanks for the comment. In Crout or Doolittle. – 2017-01-07
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    @Moo Thank you very much. I saw the result. However, it seems to me difficult to understand the theorem. – 2017-01-07
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    Yes, you can. Taking them as $1$ is just for convenience. – 2017-01-08
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    @KittyL Once upon a time, division was a relatively expensive operation to perform (both for humans and machines). So taking a diagonal 1 in $L$ or $U$ was not just for convenience but for the sake of improving the performance of the system solutions. – 2017-01-10
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    @AlgebraicPavel: I see! Thank you! – 2017-01-10
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    @AlgebraicPavel Thank you for the reply. Please write your comment as an answer. Also, if instead of 1 I am taking any other number will I get the same factorization? – 2017-01-10

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