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Prove that det A = (det P)(det S) - Mathematics Stack Exchange
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WebLieutenant Christopher M. Pupo 6/23/2012. Police Officer Richard G. Holland 3/23/2012. Police Officer Denis R. McLarney 3/1/2012. Police Officer Peter O. Rodriguez 2/12/2012. … Webdet(M) = det(A)det(C): First, We proceed by induction on n. n = 2: Obvious as det(M) = det a b 0 c = ac: n 1 )n: We take the determinant by expanding along the rst column of M. Let M~ ij be the matrix obtained from M by deleting the ith row and jth column. Jiwen He, University of Houston Math 4377/6308, Advanced Linear Algebra Spring, 2015 6 / 7 Web6. Here is one way among others: ( 0 B A 0) = ( 0 I k I k 0) ( A 0 0 B). I assume you are allowed to use the block diagonal case, which gives det A ⋅ det B for the matrix on the far right. Just in case, this follows for instance from Leibniz formula. Now it boils down to. det ( 0 I k I k 0) = ( − 1) k. This is the matrix of a permutation ... hilfe zu windows-editor in windows dark mode