Show that Ax=x is the same as (A-I)x=0. Then use the result to solve Ax=x for x

Question

Show that Ax=x is the same as (A-I)x=0.   Then use the result to solve Ax=x for x

A is the 3X3 matrix. 2 1 2.                       X is the 3X1 matrix  x1

                                2 2 -2.                                                      X2.   

                                3 1 1.                                                       X3

I also have to find Ax=4x for x.  

I don't think I really understand what is being asked.   I came up with the first part

Ax=x

Ax=Ix

Ax-Ix=0

(A-I)x=0.   

It seems to me that this is the same as Ax=0 and has only the trivial solution of x=0 no matter what the coefficient is in front of x.  Is this right?   Could someone please explain this problem for show me how to solve Ax=x for x?  

Explanation / Answer

http://sdrv.ms/1bw4EsJ

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