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Determinants for 3x3's - Method 2

This is always a bit overwhelming at first, so let's do another one:

| row 1: -3 , 4 , 6 row 2: 2 , 0 , -1 row 3: 8 , -2 , 7 | ... put a box around the second row This row will be the easiest since it has a zero!

Here are our sign box guys.  | row 1: + , - , + row 2: - , + , - row 3: + , - , + | ... put a box around the seond row

Here we go!

  | row 1: -3 , 4 , 6 row 2: 2 , 0 , -1 row 3: 8 , -2 , 7 | ... put a box around the second row                  We can ignore this chunk because of the zero!

= - ( 2 ) | row 1: 4 , 6 row 2: -2 , 7 | + ( 0 ) | who cares? | - ( -1 ) | row 1: -3 , 4 row 2: 8 , -2 |

 

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

          = -2 ( 28 + 12 ) + ( 6 - 32 ) ... = -2 ( 40 ) - 26 = -106

YOUR TURN:

| row 1: 5 , -6 , 2 row 2: 8 , -2 , 3 row 3: 10 , 3 , 0 |