Is Row Echelon Form an Upper Triangular Matrix?

[ichigo444]

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]

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.

 

[ichigo444]

Right! Thank you! This is my first post and i find this site helpful. Thanks!