Science:Math Exam Resources/Courses/MATH221/December 2009/Question 10 (b)
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Question 10 (b) 

Find the numbers b,c which make the matrix below diagonalizable. (No need to diagonalize them.)

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! 
Hint 

Science:Math Exam Resources/Courses/MATH221/December 2009/Question 10 (b)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Now let’s find the eigenvalues of b
Solve the equation above to get As similar to a, we need to make sure both eigenvalues have exactly 2 corresponding eigenvectors. When
In order to get 2 free variables, we need to set Thus When
In order to get 2 free variables, we need to set Thus 