Elementary Row Operations

Row Reduction: Row Echelon Form

Row Reduction: Reduced Row Echelon Form

Computing Determinant via Row Reduction

For a square matrix $A$:

<aside> 💡 Row reducing $A$ into row echelon form produces an upper triangular matrix with diagonal entries all 1 or some 1’s and some 0’s.

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1. Row reduce $A$ into row echelon form.
2. If the diagonal entries of the reduced matrix contain a 0, then its determinant is 0.
3. If the diagonal entries of the reduced matrix are all 1’s, its determinant is 1. Tracing back along the procedure used to row reduce using the table of how the determinant changes according to elementary row operations, we can compute the determinant of A.