text: 1. ## Finding eigenvectors
  
  The matrix A, given by
  $A=\left(\begin{array}{ccc}7&-4&6\\2&2&2\\-3&4&-2\end{array}\right)$
  
  has eigenvalues 1,2,4. Find the set of corresponding vectors.
  
  Every time I perform these operations I only get my answers as 0's. I'll geve an example.
  
  $x(A-\delta{I})=0$ taking $\delta$ as 1
  
  $\left(\begin{array}{ccc}6&-4&6\\2&1&2\\-3&4&-3\end{array}\right)$ $\left(\begin{array}{c}x\\y\\z\end{array}\right)=\l eft(\begin{array}{c}0\\0\\0\end{array}\right)$
  
  Solving
  $6x-4y+6z=0$
  $2x+y+2z=0$
  $-3x+4y-3z=0$
  
  $-x+5y-z=0$
  $x=5y-z$
  
  $30y-6z-4y+6z=0$
  $y=0$
  And so on. Could someone please direct me as to what I am doing wrong?
  
  2. Just by inspection, you can see that an eigenvector that will work is <1,0,-1>.
  
  3. You're solving the equations wrong (note that the coefficients of x and z will always vanish together if we try to sum up one equation to another) , the solutions for that eigenvalue should be x=-z
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