I know the basic rules to solve for the determinant of an $n \times n$ matrix using upper and lower triangular matrices, but what is the simplest way?

  • $\begingroup$ @robert-lewis thanks for editing. sorry for my bad english ability. $\endgroup$ – RezaOnline Nov 17 '14 at 6:32
  • $\begingroup$ What do you mean by "simplest"? Easiest to do with a pencil and paper, or easiest to do with a computer? Or perhaps the fastest to do with a computer? $\endgroup$ – Omnomnomnom Nov 17 '14 at 6:34
  • $\begingroup$ Hey, really glad to help out. Don't worry about your English, just keep writing it! Cheers! $\endgroup$ – Robert Lewis Nov 17 '14 at 6:34
  • $\begingroup$ @Omnomnomnom i mean the easiest and fastest solution for this issue. i know the main solution but i search for a better method. $\endgroup$ – RezaOnline Nov 17 '14 at 6:37
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    $\begingroup$ @RezaOnline are you aware of how to compute determinants by Gaussian elimination? You could just row-reduce until you have an upper-triangular matrix. $\endgroup$ – Omnomnomnom Nov 17 '14 at 6:43

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