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Unformatted text preview: (b) Show that the subset S ( n ) M ( n ) of symmetric matrices is a subspace. What is its dimension? (c) Show that the subset A ( n ) M ( n ) of skewsymmetric matrices is a subspace. What is its dimension? (d) Show that M ( n ) = S ( n ) + A ( n ) and S ( n ) A ( n ) = O . (3) In problem (1) above you showed that the space of innitely dierentiable functions on the unit interval is a vector space. Show that V is not nite dimensional. Hint: Consider the functions f k ( x ) = x k , k = 0 , 1 , 2 , 3 ,... . 1...
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This note was uploaded on 10/12/2009 for the course MATH 136 taught by Professor Staff during the Spring '08 term at University of Washington.
 Spring '08
 Staff
 Addition, Multiplication, Vector Space

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