SOLUTION: Matrix algebra is KILLING me! I need to know how to find the determinant for a problem like this, for example: 4 2 -3 1 -2 4 1 1

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Question 476101: Matrix algebra is KILLING me!
I need to know how to find the determinant for a problem like this, for example:

4 2 -3
1 -2 4
1 1 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help, check out this solver.

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




For more help, check out this solver.