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Coolmath Algebra
Determinants and Cramer's Rule Lesson 2 - Determinants for 3x3's -
Method 1   (page 3 of 4)
---- This algebra lesson explains a quick and easy way to find a 3x3 determinant.

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Let's do one:

| top row: 1 , 2 , 3 middle row: 4 , 5 , 6 bottom row: 7 , 8 , 9 |

| top row: 1 , 2, 3 middle row: 4 , 5 , 6 bottom row: 7 , 8, 9 | outside top row: 1 , 2 outside middle row: 4 , 5 outside bottom row: 7 , 8 ... multiply 1 , 5 , and 9 ... + ... multiply 2 , 6 , and 7 ... + ... multiply 3 , 4, and 8 ... +










| top row: 1 , 2, 3 middle row: 4 , 5 , 6 bottom row: 7 , 8, 9 | outside top row: 1 , 2 outside middle row: 4 , 5 outside bottom row: 7 , 8 ... multiply 7 , 5 , and 3 ... - ... multiply 8 , 6 , and 1 ... - ... multiply 9 , 4, and 2 ... -


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

= 45 + 84 + 96 - 105 - 48 - 72 = 0

Continued on the next page

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