(a) Let A = 5 3 -3 1 1] 3 1 -1 1 " which has characteristic polynomial C₁(x) = -(x - 2)²(x - 5). (i) From the polynomial C₁ (2) alone, what can one say about the geometric multiplicities of the eigenvalues 2 and 5? Be as specific as you can. (ii) Now find a basis for the eigenspace associated to the eigenvalue 2, and hence give the geometric multiplicity of that eigenvalue.

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