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True or false? 3. The determinant of an elementary matrix is never zero.

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vaderrrrrr | Student | Honors

Posted April 29, 2013 at 3:58 PM via web

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True or false?

3. The determinant of an elementary matrix is never zero.

Tagged with linear algebra, math

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted April 30, 2013 at 4:16 AM (Answer #1)

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True.

Because elementary matrices are a result  of identity matrices by applying elementary operations. Also an elementary matrix is invertible. And as determinant of an identity matrix is 1`!=0` . Hence the determinant of elementary matrices is non-zero.

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pramodpandey | College Teacher | Valedictorian

Posted May 1, 2013 at 4:33 AM (Answer #1)

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True.

If E is an elementary matrix, then E is invertible i.e `E^(-1)` exist. Hence

`det(E.E^(-1))=det(I_n)=1`

`det(E).det(E^(-1)=1`

`det(E)!=0`

 

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