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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