Question about row echelon form

  • Thread starter ichigo444
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Is row echelon form an upper triangular matrix? if so, does this mean that its determinant could be 1 or 0? Even if its row equivalent has a different determinant? Please Answer and thanks.
 

HallsofIvy

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Yes, a "row echelon" matrix has all "0"s below the main diagonal- "upper triangular". The numbers on the diagonal do NOT have to be "1"s.

You can always reduce a matrix to row echelon form by row operations and those may affect the determinant:

If you multiply a row by a number, the determinant is multiplied by that number.

If you swap two rows, the determinant is multiplied by -1.

If you add a multiple of one row to another, the determinant is not changed.
 
12
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Right! Thank you! This is my first post and i find this site helpful. Thanks!
 

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