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Algebra.Com's Answer #188276 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 $\"%28matrix%283%2C3%2C2%2C-3%2C0%2C4%2C1%2C3%2C0%2C5%2C22%29%29\"$ , we can see that $\"a=2\"$ , $\"b=-3\"$ , $\"c=0\"$ , $\"d=4\"$ , $\"e=1\"$ , $\"f=3\"$ , $\"g=0\"$ , $\"h=5\"$ , and $\"i=22\"$

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

$\"abs%28matrix%283%2C3%2C2%2C-3%2C0%2C4%2C1%2C3%2C0%2C5%2C22%29%29=14--264%2B0\"$ Multiply

$\"abs%28matrix%283%2C3%2C2%2C-3%2C0%2C4%2C1%2C3%2C0%2C5%2C22%29%29=278\"$ Combine like terms.

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Answer:

So $\"abs%28matrix%283%2C3%2C2%2C-3%2C0%2C4%2C1%2C3%2C0%2C5%2C22%29%29=278\"$ , which means that the determinant of the matrix $\"%28matrix%283%2C3%2C2%2C-3%2C0%2C4%2C1%2C3%2C0%2C5%2C22%29%29\"$ is 278

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