MATH152 April 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) •
Question 04 (a)
Consider the matrix
Find the eigenvalues of A (there will be two distinct eigenvalues).
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The eigenvalues of satisfy the equation
where is the identity matrix with the same dimensions as .
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To determine the eigenvalues, , of , we solve for the characteristic polynomial of for :
Thus, the eigenvalues of are .
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