SOLUTION: How do I find the determinant of K? K= 14 -13 0 3 8 -1 -10 -2 5

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Question 175530: How do I find the determinant of K?
K= 14 -13 0
3 8 -1
-10 -2 5
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%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29, we can see that a=14, b=-13, c=0, d=3, e=8, f=-1, g=-10, h=-2, and i=5

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=532--65%2B0 Multiply

abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=597 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=597, which means that the determinant of the matrix %28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29 is 597