SOLUTION: How to find determinant of 3x3 matrix

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Question 894175: How to find determinant of 3x3 matrix
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) 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%2C2%2C3%2C1%2C0%2C6%2C4%2C3%2C-2%2C5%29%29, we can see that a=2, b=3, c=1, d=0, e=6, f=4, g=3, h=-2, and i=5

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C2%2C3%2C1%2C0%2C6%2C4%2C3%2C-2%2C5%29%29=76--36%2B-18 Multiply

abs%28matrix%283%2C3%2C2%2C3%2C1%2C0%2C6%2C4%2C3%2C-2%2C5%29%29=94 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C2%2C3%2C1%2C0%2C6%2C4%2C3%2C-2%2C5%29%29=94, which means that the determinant of the matrix %28matrix%283%2C3%2C2%2C3%2C1%2C0%2C6%2C4%2C3%2C-2%2C5%29%29 is 94

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Watch this youtube video:
https://www.youtube.com/watch?v=21LWuY8i6Hw