True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.

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05-07-2022
Mathematics

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True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.

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tushargupta0691 tushargupta0691 · Answer 1 · 2022-07-14T10:43:22-04:00

The given statement is false.

What is the effect of a row operation on a determinant?

The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.

Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.

Learn more about a matrix here:

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