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(21685) 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: abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%2Aabs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29-b%2Aabs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29%2Bc%2Aabs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29

Which further breaks down to:

abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%28ei-fh%29-b%2A%28di-fg%29%2Bc%28dh-eg%29

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

abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%28ei-fh%29-b%2A%28di-fg%29%2Bc%28dh-eg%29 Start with the general 3x3 determinant.

abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=%2814%29%28%288%29%285%29-%28-1%29%28-2%29%29-%28-13%29%28%283%29%285%29-%28-1%29%28-10%29%29%2B%280%29%28%283%29%28-2%29-%288%29%28-10%29%29 Plug in the given values (see above)

abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=%2814%29%2840-2%29-%28-13%29%2815-10%29%2B%280%29%28-6--80%29 Multiply

abs%28matrix%283%2C3%2C14%2C-13%2C0%2C3%2C8%2C-1%2C-10%2C-2%2C5%29%29=%2814%29%2838%29-%28-13%29%285%29%2B%280%29%2874%29 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