document.write( "Question 222462: HI. I am having a little trouble with the 3x3 determinants. I have got the 2x2 down just fine. Here is my problem. -5 -3 2 second row 8 0 7 third row 3 2 -6. I know that I have to cancel row 1 and column 1 and solve the 2x2, but then what? Any help is greatly appreciated! Thanks!
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Algebra.Com's Answer #166566 by jim_thompson5910(35256)\"\" \"About 
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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%2C-5%2C-3%2C2%2C8%2C0%2C7%2C3%2C2%2C-6%29%29\", we can see that \"a=-5\", \"b=-3\", \"c=2\", \"d=8\", \"e=0\", \"f=7\", \"g=3\", \"h=2\", and \"i=-6\"

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

\"abs%28matrix%283%2C3%2C-5%2C-3%2C2%2C8%2C0%2C7%2C3%2C2%2C-6%29%29=70-207%2B32\" Multiply

\"abs%28matrix%283%2C3%2C-5%2C-3%2C2%2C8%2C0%2C7%2C3%2C2%2C-6%29%29=-105\" Combine like terms.


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Answer:

So \"abs%28matrix%283%2C3%2C-5%2C-3%2C2%2C8%2C0%2C7%2C3%2C2%2C-6%29%29=-105\", which means that the determinant of the matrix \"%28matrix%283%2C3%2C-5%2C-3%2C2%2C8%2C0%2C7%2C3%2C2%2C-6%29%29\" is -105
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