Question

How to use determinants in properties

Answer 1

Find the determinant by row reduction to echelon form.

  

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We now have "A" in upper triangular form. Since we have 3 pivots, "A" is invertible. If we continue the reduction process we could obtain a diagonal matrix.

 





Evidently, we only needed to go as far as echelon form to identify the values of the pivots, since the determinant is their product.