MATH221 December 2009
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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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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 .
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