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I cannot understand this statement which accompanies a standard result from Determinants and Matrices. The statement is as follows:

"If any line of a determinant D be passed over m parallel lines, the resulting determinant D' is equal to (-1)^m."

How can a determinant be passed over parallel lines?

111
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1 Answers1

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That's a strange formulation indeed, but what I think it's trying to say is that $$\det(A')=(-1)^m \det(A)$$ if the matrix $A'$ is obtained from the matrix $A$ by moving one of the rows of $A$ past $m$ other rows.

(Google “row operation determinant” if you're not familiar with this.)

Hans Lundmark
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  • Thanks! Can you also tell me if there was any mistake in asking the question? I'll keep that in mind the next time. – 111 Oct 24 '16 at 15:20
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    Not too bad for a first post! But keep in mind next time that whenever you quote something (from a book, for example), it's a good idea to give the precise source (title and author). – Hans Lundmark Oct 24 '16 at 15:22