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Question:

I've found that adding what seem to be arbitrary values in the 4th row don't change the value of the determinant. Why is that?

A = $\begin{bmatrix} 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 4 & 0 \\ 0 & 0 & 5 & 0 & 0 \\ 3 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix}$

B = $\begin{bmatrix} 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 4 & 0 \\ 0 & 0 & 5 & 0 & 0 \\ 3 & -12 & 7 & 14 & 41 \\ 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix}$

Thanks!

jackzellweger
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1 Answers1

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Replace those entries by unknowns, say $a,b,c,d$, then calculate the determinant by expanding along the first column. See what you get.

David
  • 82,662
  • I see! The variables are 0'd out by the Laplace expansion. – jackzellweger Apr 11 '16 at 02:02
  • Your question was important in me finding my answer, but it did not answer my question for me. Should I still accept your answer? – jackzellweger Apr 11 '16 at 02:04
  • @jackskis It's up to you. Some people don't like "hint" answers, others do - you can in fact find lots of debate about this on the "meta" pages. Personally, if I ask a question and somebody gives a hint which enables me to answer it, I will always upvote it and usually accept it. But it's entirely your decision. – David Apr 11 '16 at 02:14
  • Alright. I am just trying to adhere to community standards. I will accept it. – jackzellweger Apr 11 '16 at 02:16