SOLUTION: how do you calculate the determinant of 2 -3 0 4 1 3 0 5 22

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Question 256115: how do you calculate the determinant of
2 -3 0
4 1 3
0 5 22
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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