Q1 2 0 1 Let A a 2 0 where a is some real number. 0 0 1 (1) Find the eigenvalues of A. ind nd th e dim encio nof o ech oic o of
Q1 2 0 1 Let A a 2 0 where a is some real number. 0 0 1 (1) Find the eigenvalues of A. ind nd th e dim encio nof o ech oic o of
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Transcribed Image Text:Q1
Г2 0 1
Let A
2 0
where a is some real number.
0.
1
(1) Find the eigenvalues of A.
(2) Find a basis and the dimension of each eigenspace of A.
(Warning: your answer should depend on a)
(3) Find all values of a for which A has an eigenbasis and write it
down. (Here, an eigenbasis is a basis of R' consisting of three
linearly independent eigenvectors of A)
Show your work/Justify your answers!
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