Question 4: The 3x3 matrix M is given below, in term of a constant k: k 21 M = 4 3. 2 1-2 -1 a) Show that 2ı = 1 is an eigenvalue of M for all values of k. b) Given that -2 is an eigenvector of M with corresponding eigenvalue 22 # 1, find the value of 22 and the value of k. c) Find the value of the third eigenvalue of M.

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Question 4: The 3x3 matrix M is given below, in term of a constant k:
k
21
M =
4
3
2
-2
-1
a) Show that 2ı = 1 is an eigenvalue of M for all values of k.
b) Given that -2 is an eigenvector of M with corresponding eigenvalue 22 # 1, find
the value of 22 and the value of k.
c) Find the value of the third eigenvalue of M.
Transcribed Image Text:Question 4: The 3x3 matrix M is given below, in term of a constant k: k 21 M = 4 3 2 -2 -1 a) Show that 2ı = 1 is an eigenvalue of M for all values of k. b) Given that -2 is an eigenvector of M with corresponding eigenvalue 22 # 1, find the value of 22 and the value of k. c) Find the value of the third eigenvalue of M.
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