Suppose that ,...., are distinct eigenvalues of matrix A with corresponding eigenvectors x₁,x₂,...,x, respectively. Show that x₁,x₂,....x, are linearly independent.

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Q: (b) Find all subgroups of (Z/2)×2 = Z/2 × Z/2.

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Q: b 1 b 1 ..... 2 3 GRAPH A GRAPH B d GRAPH A 2 3 GRAPH B b d GRAPH A 1 i 2 5 3 GRAPH B

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Q: Prove that if f(z) is analytic, then: [f'(2)² = (² |f' (2) 1³² = (²+ (²)² = (²+)²

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Q: (p) = p - 1 if p is prime (pk) = pk - pk-1 = pk (1 − 2) if p is prime and k ≥ 1

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