SOLUTION: evaluate the determinant 3 -1 2 -2 1 -3 4 -1 3

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Question 220975: evaluate the determinant
3 -1 2
-2 1 -3
4 -1 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2C-1%2C2%2C-2%2C1%2C-3%2C4%2C-1%2C3%29%29, we can see that a=3, b=-1, c=2, d=-2, e=1, f=-3, g=4, h=-1, and i=3

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C3%2C-1%2C2%2C-2%2C1%2C-3%2C4%2C-1%2C3%29%29=0--6%2B-4 Multiply

abs%28matrix%283%2C3%2C3%2C-1%2C2%2C-2%2C1%2C-3%2C4%2C-1%2C3%29%29=2 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C3%2C-1%2C2%2C-2%2C1%2C-3%2C4%2C-1%2C3%29%29=2, which means that the determinant of the matrix %28matrix%283%2C3%2C3%2C-1%2C2%2C-2%2C1%2C-3%2C4%2C-1%2C3%29%29 is 2