Q4. Using Proposition 8.3.2 from the notes, we can rewrite Question 2b from Written Assignment 7 as the following lemma

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Q4 Using Proposition 8 3 2 From The Notes We Can Rewrite Question 2b From Written Assignment 7 As The Following Lemma 1 (37.73 KiB) Viewed 11 times

Q4. Using Proposition 8.3.2 from the notes, we can rewrite Question 2b from Written Assignment 7 as the following lemma (do not prove this): Lemma 1. Let A € M₂(F). If v₁ and 2 are eigenvectors of A with distinct eigenvalues X₁ and X2, then the set {1, 2} is linearly independent. Now let A € M₁ (F), and let 7₁, 72, and 73 be eigenvectors of A with pairwise distinct eigenvalues A₁, A₂ and A3 (in other words, A; ‡ Aj for all i ‡ j). Prove that the set {71, 72, 73} is linearly independent. You may use Lemma 1 in your proof.