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Unformatted text preview: rank( AB ) ≤ rank( B ). Q8. A 2 × 2 matrix A has eigenvalues λ 1 = 1 and λ 2 = 2 with respective eigenvectors (1 , 1) T and (1 , 2) T . Write the vector v = (1 , 0) T as a linear combination of these eigenvectors and then ﬁnd A 4 v . Q9. Let L 1 : V → V be a linear transformation. Deﬁne L : V → V by L ( v ) = L 1 ( L 1 ( v )) , v ∈ V. Prove that L is a linear transformation. Q10. If A and B are similar matrices, prove that A T and B T are similar. 2...
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 Fall '08
 boas
 Math, Linear Algebra, Algebra, Matrices, linear transformation, Q9. Let L1

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