Example:

|1 2 3|

|4 5 6|

|7 8 9|

The normal formula for the determinant of a 3 by 3 matrix would be

det=1(5x9-6x8)-2(4x9-6x7)+3(4x8-5x7)

det=45-48-2(36-42)+3(32-35)

det=0

However we can solve this in a more arbitrary fashion utilizing a different row than the top row

det=-4(2x9-3x8)+5(1x9-3x7)-6(1x8-2x7)

det=-4(18-24)+5(9-21)-6(8-14)

det=0

Or by the last row

det=7(2x6-3x5)-8(1x6-3x4)+9(1x5-2x4)

det=7(12-15)-8(6-12)+9(5-8)

det=0

This can be used to make it easier to solve determinants by finding the simplest pattern to solve for the determinant.

|0 0 2 3 1|

|0 0 0 2 2|

|0 9 7 9 3|

|0 0 0 0 5|

|3 4 5 8 5|

-5

|0 0 2 3|

|0 0 0 2|

|0 9 7 9|

|3 4 5 8|

-5(2)

|0 0 2|

|0 9 7|

|3 4 5|

-5(2)(2)

|0 9|

|3 4|

-5(2)(2)(0x4-3x9)

det=540

## No comments:

## Post a Comment