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...Determinants terrya loring a row operation by product thedeterminant is best understood in terms of operations my opinion most books start dening the determinant via formulas that are nearly impossible to use except on very small matrices since what taught rst often learned this dangerous wewill with idea square matrix single number can be calculated as side gaussian elimination performed you already know it takes calculate extra keeping track some magic numbers multiply at together create another called how mathematicians came discover these topic denition we dene factor every follows type assmuption i j k rj rk ii iii det an n singular b identity c if non then factors sequence reduces notation or generally one drops braces using so outer parantheses dropped notations used notice means any series like ends skipping not theoretical class reasoning shows comes out same no matter example find r y have conclude original invertible do need advance nd always lead less than pivots and op...