Eigenvalues + shit (remedy a shitty textbook)

Help, my textbook sucks and has no examples on this type of problem.

Assume A is the weird eigenvalue symbol.
Find a 3x3 symmetric matrix that has eigenvalues A1=1,A2=3,A3=5 and the corresponding eigenvectors K1=(1;-1;1),K2=(1;0;-1),K3=(1;2;1).

I can easily do the reverse (find eigenvalues/vectors given a matrix), but have no clue where to even start here.  Any help?

>>2
Shit, how did you make that matrix?, what the syntax?