SOLUTION: compute the determinant 3 0 -1 6 -1 4 2 -2 -2

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Question 871631: compute the determinant
3 0 -1
6 -1 4
2 -2 -2
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
|3, 0,-1|
|6,-1, 4|=40
|2,-2,-2|
Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix

If you have the general 3x3 matrix:

%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

the determinant is:

Which further breaks down to:



Note: abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29, abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29 and abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 are determinants themselves.
If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver

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From the matrix %28matrix%283%2C3%2C3%2C0%2C-1%2C6%2C-1%2C4%2C2%2C-2%2C-2%29%29, we can see that a=3, b=0, c=-1, d=6, e=-1, f=4, g=2, h=-2, and i=-2

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C3%2C0%2C-1%2C6%2C-1%2C4%2C2%2C-2%2C-2%29%29=30-0%2B10 Multiply

abs%28matrix%283%2C3%2C3%2C0%2C-1%2C6%2C-1%2C4%2C2%2C-2%2C-2%29%29=40 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C3%2C0%2C-1%2C6%2C-1%2C4%2C2%2C-2%2C-2%29%29=40, which means that the determinant of the matrix %28matrix%283%2C3%2C3%2C0%2C-1%2C6%2C-1%2C4%2C2%2C-2%2C-2%29%29 is 40