Science:Math Exam Resources/Courses/MATH307/April 2010/Question 01 (a)
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Question 01 (a) 

Mark each statement as true or false and give a general explanation (3 and a third points per part). If you decide that a statement is false, you can give a contradicting example instead. Bear in mind that to mark a statement true all of its parts must be true. It is given that a real matrix A is a root of the equation Failed to parse (syntax error): {\displaystyle \displaystyle A^n − A = 0 } with an integer. Then it is possible to conclude the following. The size of A is because by the Cayley  Hamilton theorem A satisfies , with being the characteristic polynomial of A. Since it is given that A is a root of an nth degree polynomial, its characteristic polynomial must be of degree n and thus A is . 
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/MATH307/April 2010/Question 01 (a)/Hint 1 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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