INTRODUCTORY LINEAR ALGEBRA/VECTORS AND SUBSPACES EXAM STUDY GUIDE 2024

Without distinguishing row and column vectors, we can define vectors as follows: A special type of vector is the standard vector. However, in linear algebra, we sometimes need to distinguish row and column vectors, which are defined as follows: The two basic vector operations are addition and scalar multiplication. Using these two operations only, we can combine multiple vectors as in the following definition. Another concept that is closely related to linear combinations is span. The cross-hatched plane is the span of and in . Example. The span of the set is since linear combinations of Geometrically, the span is a plane in and . are in the form of The span of the set is Exercise. 1 Select all correct expression(s) for , in which . . Empty set, . . . 2 Select all correct expression(s) for , in which are column vectors. . . . . 3 Let and be sets containing some vectors, which are nonempty subset of . Select all correct statement(s). If , then . If , then for each Submit Linear independence