How to find eigen value and eigen vectors of a matrix

4
hi friends

 i need to know how to find eigen value and eigen vector of a matrix

e.g matrix

3 10 5
-2 3 -4
3 5 7

kindly explain with detailed steps

~thanks
I Hope the Question is Incorrect or Wrong.. I Solved the Question, but Getting Eigenvector as Zero...

Note that an eigenvector cannot be 0, but an eigenvalue can be 0.

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sorry Srini,

The matrix is

3 10 5
-2 -3 -4
3 5 7

can you explain me the step by step procedure for solving eigen vectors alone ( As i am little unclear where cross multiplication are used )

and eigen values are 2,2,3

    How to find eigen value and eigen vectors of a matrix