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

Find the number a which make the matrix below diagonalizable. (No need to diagonalize them.)

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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 (a)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. For an n by n matrix to be diagonalizable, the matrix must have n distinct eigenvectors. First let’s find the eigenvalues of a
Solve the equation above to get We got a double root here, so we need to have 2 corresponding eigenvectors for . When
In order to have 2 eigenvectors, we need to have 2 free variables here i.e. we need to have Solve this to get . 