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Unformatted text preview: 1 3 1 2 1 1 . (i) Find the rank and the nullity of the matrix B . (ii) Find a basis for the row space of B , then extend this basis to a basis for R 4 . (iii) Find a basis for the nullspace of B . Bonus Problem 5 (15 pts.) Show that the functions f 1 ( x ) = x , f 2 ( x ) = xe x , and f 3 ( x ) = e-x are linearly independent in the vector space C ( R ). Bonus Problem 6 (15 pts.) Let V be a nite-dimensional vector space and V be a proper subspace of V (where proper means that V n = V ). Prove that dim V < dim V ....
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This note was uploaded on 02/13/2012 for the course MATH 304 taught by Professor Hobbs during the Spring '08 term at Texas A&M.
- Spring '08