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Question 150529: if two rows of a determinant are interchanged, what is true of the resulting determinant?: if two rows of a determinant are interchanged, what is true of the resulting determinant?
Answer by Edwin McCravy(2043) About Me  (Show Source):
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if two rows of a determinant are interchanged, what is true of the resulting determinant?

The sign is changed.
Illustration:
abs(matrix(2,2,2,-7,-4,5))=2*5-(-7)*(-4)=10-28=-18
abs(matrix(2,2,-4,5,2,-7))=(-4)*(-7)*(-4)=28-10=18
In general just for a 2x2 matrix.
abs(matrix(2,2,a,b,c,d))=ad-bc
abs(matrix(2,2,c,d,a,b))=cb-da=bc-ad= -ad+bc=-(ad-bc)
Edwin