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# (Solved): Matrix A is factored in the form PDP^(-1). Use the Diagonalization Theorem to find the eigenvalues o ...

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

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