Matrix Determinant Example-2

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6. Matrix Determinant example ( Enter your problem )

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Definition and Examples
Example-2

Other related methods

1. Definition and Examples
(Previous example)

7. Adjoint of a matrix
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2. Example-2

1. Find `| A |` ...
`A=[[1,2],[4,5]]`

Solution:

`|A|`

	`1`	`2`
	`4`	`5`

`=1 × 5 - 2 × 4`

`=5 -8`

`=-3`

2. Find `| A |` ...
`A=[[1,2,3],[4,5,6],[7,8,9]]`

Solution:

`|A|`

`1`	`2`	`3`
`4`	`5`	`6`
`7`	`8`	`9`

`1`

	`5`	`6`
	`8`	`9`

`-2`

	`4`	`6`
	`7`	`9`

`+3`

	`4`	`5`
	`7`	`8`

`=1 xx (5 × 9 - 6 × 8) -2 xx (4 × 9 - 6 × 7) +3 xx (4 × 8 - 5 × 7)`

`=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)`

`=1 xx (-3) -2 xx (-6) +3 xx (-3)`

`= -3 +12 -9`

`=0`

This material is intended as a summary. Use your textbook for detail explanation.
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