Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (h)
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Question 12 (h) 

If a matrix A has distinct eigenvalues, then . 
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Hint 

Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (h)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The answer is false. Consider the matrix
A has two distinct eigenvalues, 0 and 1. However, clearly A has only one linearly independent column, so 