## Properties of Determinants Part 6

more about this property…

P9: The determinant of a product is the product of the determinants.

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## Properties of Determinants Part 6

## Properties of Determinants Part 5

## Properties of Determinants Part 4

## Properties of Determinants Part 3

## Properties of Determinants – Part 2

## Properties of Determinants – Part 1

more about this property…

P9: The determinant of a product is the product of the determinants.

really practical property

P9: The determinant of a product is the product of the determinants.

yet another property of determinants

P8: If a matrix is singular its determinant is zero, if it is invertible then its determinant is not zero.

Important Consequence: The determinant is plus or minus the product of its pivots.

two more properties of determinants

P6: If a matrix contains a row of zeros then its determinant is zero.

P7: If a matrix is triangular, then its determinant is the product of the diagonal entries.

Two more properties:

P4: If two rows are equal then the determinant is zero.

P5: Adding a multiple of one row to another row doesn’t change the determinant.

Defining Properties of the Determinant

P1: The determinant of the identity matrix is 1.

P2: Interchanging two row changes the sign of the determinant.

P3: The determinant is a linear function of its rows – taken one row at a time.