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Determinant Properties


The determinants associated with square order matrices no have the following properties:

P1) When all elements of a row (row or column) are null, the determinant of this matrix is ​​null. Example:

P2) If two rows of an array are equal, then their determinant is null. Example:

P3) If two parallel rows of a matrix are proportional, then their determinant is null. Example:

P4) If the elements of a row in a matrix are linear combinations of the corresponding elements of parallel rows, then their determinant is null. Examples:

P5) Jacobi's theorem: The determinant of a matrix does not change when we add to the elements of a row a linear combination of the corresponding elements of parallel rows. Example:

Replacing the 1st column with the sum of that same column twice the 2nd, we have:

Next: Properties (Part 2)