Question

Matrix A is factored in the form PDP Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 1 1 2 2 1 2 4 2 2 8 5 0 0 A= 1 2 2 = 2 0-2 0 1 0 1 4 1 4 1 2 1 1 3 2 -1 0 0 0 1 1 8 3 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 2 = A basis for the corresponding eigenspace is { } OB. In ascending order, the two distinct eigenvalues are 14 = and 1 = Bases for the corresponding eigenspaces are { } and {}, respectively. C. In ascending order, the three distinct eigenvalues are 14 = 12 = and 13 = Bases for the corresponding eigenspaces are {}, }, and { }, respectively.

Answer 1

I have done it for you in detail. Kindly go through. In C part we don't have 3 distinct eigen values. So the question is wrong.

h the 2 2 2 O A. 2 12 1 2 2 1 3 0-2 - 2 -1 O 8 POP! OA. There is one distinct eigenvalue 2-5 A basis for the corresponding eigensface is S12 2 2 and 2:15 o B. In ascending order, the too distinct eigenvalues are 2,- Basts for the corresponding eigensfaces and respectively. are 2 {[:] -2 {0] -values oc. In ascending order, the three distinct eigen- are 9,- O, 2,- , 22-0,... This question is wrong We do not have 3 distinctinct eigenvalues Only Colistinct) I and 5. where ultiplicity + 2 eigenvalues I had multiplicity ? as 5 bas multi