
find this eigenvalue
Find corresponding eigenvalue
given: A= 2 1 1 x=1
1 2 1 1
1 1 2 1
I figured that this matrix multiplied with that vector results in zero, hence eigenvalue can be zero, but I also figured that eigenvalue can be 3. Im now confused about possible eigenvalue. Help plz

a matrix can (and usually does) have more than one eigenvalue.
in this case, all you need to do is find the particular eigenvalue for a particular eigenvector, which you have done.

If <1, 1, 1> is, in fact, an eigenvector for this matrix, then, by definition of "eigenvector", we must have
[2 1 1][1] [1]
[1 2 1][1]= L[1]
[1 1 2][1] [1]
Multiply the left side and see if it does give a multiple of <1, 1, 1> and what that multiple is.
You did not need to calculate the possible eigenvalues in advance to do that.