hw02 - w ∈ Span S has a unique expression as a linear...

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Math 110—Linear Algebra Fall 2009, Haiman Problem Set 2 Due Monday, Sept. 14 at the beginning of lecture. 1. Section 1.5, Exercise 3. 2. Let S be the subset { sin 2 ( x ) , sin(2 x ) , cos(2 x ) , 1 } of the vector space F ( R , R ). Which subsets of S are linearly dependent and which are linearly independent? 3. Prove that if S = { v 1 , . . . , v n } is a finite, linearly independent set of vectors in a vector space V , then every vector
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Unformatted text preview: w ∈ Span( S ) has a unique expression as a linear combination a 1 v 1 + ··· + a n v n . 4. Find a basis of the subspace of symmetric matrices in M 3 × 3 ( R ). What is the dimension of this subspace? 5. Prove that if V is a vector space over F 2 with finite dimension n , then V is a finite set. How many elements does it have?...
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