Unformatted text preview: (b) Show that the subset S ( n ) ⊂ M ( n ) of symmetric matrices is a subspace. What is it’s dimension? (c) Show that the subset A ( n ) ⊂ M ( n ) of skewsymmetric matrices is a subspace. What is it’s 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 inﬁnitely diﬀerentiable functions on the unit interval is a vector space. Show that V is not ﬁnite dimensional. Hint: Consider the functions f k ( x ) = x k , k = 0 , 1 , 2 , 3 ,... . 1...
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 Spring '08
 Staff
 Addition, Multiplication, Vector Space, lang., infinitely differentiable functions

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