SOLUTION: find the value of |5...3..-2| |1...0...4| |4...1...2|

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Question 211775: find the value of
|5...3..-2|
|1...0...4|
|4...1...2|
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%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29, we can see that a=5, b=3, c=-2, d=1, e=0, f=4, g=4, h=1, and i=2

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%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=%285%29%28%280%29%282%29-%284%29%281%29%29-%283%29%28%281%29%282%29-%284%29%284%29%29%2B%28-2%29%28%281%29%281%29-%280%29%284%29%29 Plug in the given values (see above)

abs%28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=%285%29%280-4%29-%283%29%282-16%29%2B%28-2%29%281-0%29 Multiply

abs%28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=%285%29%28-4%29-%283%29%28-14%29%2B%28-2%29%281%29 Subtract

abs%28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=-20--42%2B-2 Multiply

abs%28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=20 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29=20, which means that the determinant of the matrix %28matrix%283%2C3%2C5%2C3%2C-2%2C1%2C0%2C4%2C4%2C1%2C2%29%29 is 20