Is Row Echelon Form an Upper Triangular Matrix?

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Row echelon form (REF) is indeed classified as an upper triangular matrix, characterized by zeros below the main diagonal. The determinant of a matrix in REF can be either 1 or 0, depending on the values along the diagonal, which do not need to be 1s. Row operations such as multiplying a row by a scalar or swapping rows affect the determinant, while adding a multiple of one row to another does not change it. Understanding these properties is crucial for matrix manipulation and determinant calculations.

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

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