document.write( "Question 476101: Matrix algebra is KILLING me!\r
\n" ); document.write( "\n" ); document.write( " I need to know how to find the determinant for a problem like this, for example:\r
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Algebra.Com's Answer #326485 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 $\"%28matrix%283%2C3%2C4%2C2%2C-3%2C1%2C-2%2C4%2C1%2C1%2C1%29%29\"$ , we can see that $\"a=4\"$ , $\"b=2\"$ , $\"c=-3\"$ , $\"d=1\"$ , $\"e=-2\"$ , $\"f=4\"$ , $\"g=1\"$ , $\"h=1\"$ , and $\"i=1\"$

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

$\"abs%28matrix%283%2C3%2C4%2C2%2C-3%2C1%2C-2%2C4%2C1%2C1%2C1%29%29=-24--6%2B-9\"$ Multiply

$\"abs%28matrix%283%2C3%2C4%2C2%2C-3%2C1%2C-2%2C4%2C1%2C1%2C1%29%29=-27\"$ Combine like terms.

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Answer:

So $\"abs%28matrix%283%2C3%2C4%2C2%2C-3%2C1%2C-2%2C4%2C1%2C1%2C1%29%29=-27\"$ , which means that the determinant of the matrix $\"%28matrix%283%2C3%2C4%2C2%2C-3%2C1%2C-2%2C4%2C1%2C1%2C1%29%29\"$ is -27

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