Give an example of a 3x3 matrix having only two eigenvalues, one with corresponding eigenspace of dimension one and the other with corresponding eigenspace of dimension two. I need to also justify my answer by finding a basis for each eigenspace.

A=[0 0 60

      1 0 7

      0 1 -6]

How can I find the eigenvalues and a correspnding eigenvector for each eigenvalue for A^5.(A to fifth power)

u:=Vector([1,1,-1]),v:=Vector([2,0,-5]),w:=Vector([5,1,-11]) (Vectors are by columns)

How can I find a basis for the subspace spanned by {u,v,w}.

S={v1=[-4 v2=[7 v3=[-3 v4=[-6 v5=[1 }
           -2       1        3        -6       3
           -1      -2        0        -1       4

u=[-2        v=[ 1           w=[3

      -5             7a               3

       5]             -2]              a]