QUESTION 1. Assume A, B are similar n x n matrices, say A = Q-BQ. (i)...

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QUESTION 1. Assume A, B are similar n x n matrices, say A = Q-¹BQ. (i) We know С₁(a) = CB(a). Prove m₁(a) = mB(a). (ii) Assume that a is an eigenvalue of A and {v₁, v2, ..., Uk} is a basis for Ea (A). Prove that {Qu₁, Qu2,..., QUk} is a basis for Ea (B). [Hint: Observe that BQ = QA and since Q is invertible, Qw = On iff w = On] QUESTION 1. Assume A, B are similar n x n matrices, say A = Q-¹BQ. (i) We know С₁(a) = CB(a). Prove m₁(a) = mB(a). (ii) Assume that a is an eigenvalue of A and {v₁, v2, ..., Uk} is a basis for Ea (A). Prove that {Qu₁, Qu2,..., QUk} is a basis for Ea (B). [Hint: Observe that BQ = QA and since Q is invertible, Qw = On iff w = On]