The concept of a determinant also does not exist in traditional algebra. It is also difficult to explain the meaning of a determinant in any intuitive fashion. A determinant is only defined for a square matrix and is the result of a series of calculations resulting in a scalar. It is the sum of a series of products of the elements of the matrix and each product is multiplied by +1 or -1 according to certain rules. For example, for a 2 x 2 matrix, the determinant is found by taking the difference between the products of the diagonals versus the off-diagonals. That is, the determinant of matrix |A| = (au*a22) - (a12*a21).

the determinant is calculated as (7 x 6) - (4 x 3) = 30.

A determinant for a 3 x 3 matrix follows similar, but more complicated, rules. As the order of the matrices gets larger the calculations become increasingly complex. Again, however, there are computer programs to evaluate the determinant of a matrix.

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