Matrix A is factored in the form
PDP^(-1)
. Use the Diagonalization Theorem to find the eigenvalues of
A
and a basis for each eigenspace.
A=[[2,0,-12],[6,4,36],[0,0,4]]=[[-6,0,-1],[0,1,3],[1,0,0]][[4,0,0],[0,4,0],[0,0,2]][[0,0,1],[3,1,18],[-1,0,-6]]
Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue,
\lambda =
◻
A basis for the corresponding eigenspace is
◻
B. In ascending order, the two distinct eigenvalues are
\lambda _(1)=
◻
and
\lambda _(2)=
◻
Bases for the corresponding eigenspaces are
◻
and
◻
respectively. C. In ascending order, the three distinct eigenvalues are
\lambda _(1)=
◻
\lambda _(2)=
◻
and
\lambda _(3)=
◻
Bases for the corresponding eigenspaces are {
◻
, and
◻
respectively