Question: [2 marks ] [; marks ] [2 marks ] 7. Write your solutions for this question on the Answer Sheets, Page 3 Let A be

[2 marks ] [; marks ] [2 marks ] 7. Write your solutions for this question on the Answer Sheets, Page 3 Let A be a square matrix of order 3. Suppose that the eigenvalues of A are 2 and 7, and the respective eigenspaces are given by Z _l_ _l E2(A)=Span _: l __ ,.r;?[A)=Span _: l :5: 2 _l_ _l l (a) Find the respective algebraic multiplicities m2(A) and m?(A') of the eigenvalues 2 and 7 ofA. (b) Find a diagonal matrix D and an invertible matrix P of order 3 such that P '1AP : D (you do 11014 need to verify this identity). (c) Find the determinant of A

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