This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A subspace of a vector space V is a subset H of V such that 1. the zero vector is in H , 2. the sum of two vectors in H is again in H , and 3. any scalar times any vector in H is again in H . EXAMPLES. Determine whether the following are subspaces of an appropriate vector space. • Span { v 1 ,..., v p } , where the vectors all belong to some vector space V • The set K of all polynomials of degree at most 5 whose value at 1 is 0. • All vectors of the form 3 2 ab 3 a + 2 b • The set H of all vectors of the form 9 a5 b 2 a 3 a + 2 b HOMEWORK: SECTION 4.1...
View
Full Document
 Spring '08
 PAVLOVIC
 Algebra, Derivative, Vector Space, Ring

Click to edit the document details