SOLUTION: what is the value of the determinant? 3 6 8 2 4 0 3 6 8

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Question 262916: what is the value of the determinant?
3 6 8
2 4 0
3 6 8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that two rows are identical. This means that the determinant must be zero. However, let's use another method.

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%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29, we can see that a=3, b=6, c=8, d=2, e=4, f=0, g=3, h=6, and i=8

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=96-96%2B0 Multiply

abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=0 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29=0, which means that the determinant of the matrix %28matrix%283%2C3%2C3%2C6%2C8%2C2%2C4%2C0%2C3%2C6%2C8%29%29 is 0