hw2sol - MATH 223 - HOMEWORK #2 Solutions Problem 1....

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Unformatted text preview: MATH 223 - HOMEWORK #2 Solutions Problem 1. 8(a,b,f) in Section 1.3. A subspace is defined by linear equations with right hand side equal to zero. The equations in (a) are of this type if we bring all a-s to one side. The equations in (b) and (f) do not define a subspace. For example, (b) has no zero element; (f) is not closed under addition and scalar multiplication. Problem 2. 11 in in Section 1.3. It is not a subspace because the sum of two polynomials of degree n can have degree less than n , so the sum does not lie in the subspace. Problem 3. Let P 7 be the vector space of polynomials of degree 7 or less. Define W = { p ( x ) P 7 | p (1) = p (2) = ... = p (5) = 0 } . (1)Show that W is a subspace of P 7 . The three conditions for the subspace are easy to check. (2)What is the intersection W P 4 ? (Recall how many zeroes can a polynomial of degree 4 have.) The intersection is the zero space { } because the only degree 4 polynomial that has 5 roots is the zero polynomial....
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This note was uploaded on 02/01/2010 for the course MATH math115a taught by Professor Shalom during the Spring '10 term at UCLA.

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hw2sol - MATH 223 - HOMEWORK #2 Solutions Problem 1....

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