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Algebra.Com's Answer #569125 by MathLover1(20850) $\"\"$ $\"About$

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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 $\"%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29\"$ , we can see that $\"a=-2\"$ , $\"b=5\"$ , $\"c=4\"$ , $\"d=3\"$ , $\"e=-2\"$ , $\"f=1\"$ , $\"g=1\"$ , $\"h=6\"$ , and $\"i=-3\"$

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

$\"abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=0--50%2B80\"$ Multiply

$\"abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=130\"$ Combine like terms.

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Answer:

So $\"abs%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29=130\"$ , which means that the determinant of the matrix $\"%28matrix%283%2C3%2C-2%2C5%2C4%2C3%2C-2%2C1%2C1%2C6%2C-3%29%29\"$ is 130

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