document.write( "Question 274498: Evaluate the determinant:\r
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Algebra.Com's Answer #200301 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%2C3%2C3%2C4%2C6%2C1%2C2%2C3%2C2%2C2%29%29\", we can see that \"a=3\", \"b=3\", \"c=4\", \"d=6\", \"e=1\", \"f=2\", \"g=3\", \"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%2C3%2C4%2C6%2C1%2C2%2C3%2C2%2C2%29%29=-6-18%2B36\" Multiply

\"abs%28matrix%283%2C3%2C3%2C3%2C4%2C6%2C1%2C2%2C3%2C2%2C2%29%29=12\" Combine like terms.


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Answer:

So \"abs%28matrix%283%2C3%2C3%2C3%2C4%2C6%2C1%2C2%2C3%2C2%2C2%29%29=12\", which means that the determinant of the matrix \"%28matrix%283%2C3%2C3%2C3%2C4%2C6%2C1%2C2%2C3%2C2%2C2%29%29\" is 12
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