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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 as 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.
 Spring '10
 SHALOM
 Linear Algebra, Algebra, Linear Equations, Equations

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