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Determinants for 3x3's - Method 2

Now do the last guy in the column:

| row 1: -2 , -9 , 4 row 2: 3 , 7 , -5 row 3: 1 , -6 , 8 | ... circle the 1 and cross out his row and column

= + ( -2 ) | row 1: 7 , -5 row 2: -6 , 8 | - ( 3 ) | row 1: -9 , 4 row 2: -6 , 8 | + ( 1 ) | row 1: -9 , 4 row 2: 7 , -5 |
 

Now, just pop the determinants and clean it up!

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

Be careful!  It's easy to make little boo-boos!
 

            = -2 ( 56 - 30 ) - 3 ( -72 + 24 ) + ( 45 - 28 )
 

            = -2 ( 26 ) - 3 ( -48 ) + 17 = 109 ... Whew!