SOLUTION: How do i find the determinant? (2)(-1)(4) (8)(3)(-5) (-5)(2)(2)

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: How do i find the determinant? (2)(-1)(4) (8)(3)(-5) (-5)(2)(2)      Log On


   

Question 184670: How do i find the determinant?
(2)(-1)(4)
(8)(3)(-5)
(-5)(2)(2)
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-1%2C4%2C8%2C3%2C-5%2C-5%2C2%2C2%29%29, we can see that a=2, b=-1, c=4, d=8, e=3, f=-5, g=-5, h=2, and i=2

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C2%2C-1%2C4%2C8%2C3%2C-5%2C-5%2C2%2C2%29%29=32-9%2B124 Multiply

abs%28matrix%283%2C3%2C2%2C-1%2C4%2C8%2C3%2C-5%2C-5%2C2%2C2%29%29=147 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C2%2C-1%2C4%2C8%2C3%2C-5%2C-5%2C2%2C2%29%29=147, which means that the determinant of the matrix %28matrix%283%2C3%2C2%2C-1%2C4%2C8%2C3%2C-5%2C-5%2C2%2C2%29%29 is 147