Applied Mathematics 1411A/B Lecture Notes - Lecture 11: Feasible Region, Linear Combination
12 Mar 2015
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Recall: last day, we introduced the concept of a subspace: If u and v are vectors in w, then. If k is any scalar and u is any vector in w, then uk is in w vu is in w. 2: is the set of all vectors of the form (a, b, 0) with b a. 3 a subspace of r3: is the set of all polynomials of the form a xaxa. Theorem (solution space of homogeneous systems): if linear system of m equations in n unknowns, then the set of solution vectors is a subspace of. Example: consider with a as given below. is a homogeneous. Definition: a vector w is called a linear combination of the vectors can be expressed in the form where. 3 is a linear combination of u and v and that. 1 are vectors in a vector space v, then: rv. 2: then set w of all linear combinations of vv.
