To evaluate a 3x3 determinant, you multiply 3 numbers together
6 times. as indicated by the numbers in red below, changing
the signs of some, and then combine all 6 numbers:
If two (or all three) of the numbers multiplied go downhill to
the right like this \, you KEEP the sign.
If two (or all three) of the numbers multiplied go downhill to the
left like this /, you CHANGE the sign.
|5 0 1|
|4 1 2| (5)(1)(0) = 0 (keep the sign) +0
|2 5 0|
|5 0 1|
|4 1 2| (0)(2)(2) = 0 (keep the sign) +0
|2 5 0|
|5 0 1|
|4 1 2| (1)(4)(5) = 20 (keep the sign) +20
|2 5 0|
|5 0 1|
|4 1 2| (1)(1)(2) = 2 (change the sign) -2
|2 5 0|
|5 0 1|
|4 1 2| (0)(4)(0) = 0 (change the sign) -0
|2 5 0|
|5 0 1|
|4 1 2| (5)(2)(5) = 50 (change the sign) -50
|2 5 0|
----------------------------------------------------------------------------
Now add all those 6 numbers up: 0+0+20-2-0-50 = -32
Answer: -32
Edwin
