Unformatted text preview: L . (They need not be a basis.) (c) Find a matrix A such that L ( x ) = A x . (d) What is the dimension of the range of L ? Give a reason for your answer. 3. (10 pts) Suppose that A, B ∈ R n × n are nonsingular and that A and B are similar. Prove that A1 and B1 are similar. 4. (10 pts) Suppose V is a subspace of R n and W is a subspace of V . Prove that W ⊥ contains V ⊥ . WARNING: The ﬁnal exam will probably not be in this room. END OF EXAM...
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 Winter '07
 Enright
 Math, Linear Algebra, Algebra, 6 pts, blue book, 10 pts, 24 pts

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