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Question 927971:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

first find determinant:
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%2C1%2C1%2C2%2C1%2C0%2C1%2C2%2C1%2C3%29%29, we can see that a=1, b=1, c=2, d=1, e=0, f=1, g=2, h=1, and i=3

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C1%2C1%2C2%2C1%2C0%2C1%2C2%2C1%2C3%29%29=-1-1%2B2 Multiply

abs%28matrix%283%2C3%2C1%2C1%2C2%2C1%2C0%2C1%2C2%2C1%2C3%29%29=0 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C1%2C1%2C2%2C1%2C0%2C1%2C2%2C1%2C3%29%29=0, which means that the determinant of the matrix %28matrix%283%2C3%2C1%2C1%2C2%2C1%2C0%2C1%2C2%2C1%2C3%29%29 is 0



the determinant is zero it means the system has either no+solution or infinite+solutions