Linear Algebra Worksheet 2 Math 108A Fall 2009, TA Grace Kennedy Summary: Linear Algebra Worksheet 2 Math 108A Fall 2009, TA Grace Kennedy NAME: Course Website: http://math.ucsb.edu/kgracekennedy/F09108A.html Supplemental Reading: Axler pages 21-34 Span, Linear Independence, Basis, and Dimension Here, F represents a field. And V is a vector space of finite dimension n. 1. Prove of disprove the following statements. (a) If {v1, . . . , vm+1} V is linearly dependent, then so is {v1, . . . , vm-1}. (b) Any subset of linearly independent vectors is linearly independent. (c) Any collection of n + 1 vectors {v1, . . . , vn+1} V is linearly depen- dent. (d) A finite dimensional vector space has a finite number of elements. (e) If W is another n-dimensional vector space, then there exists a bijec- tion between W and V .1 2. (From Axler page 35) Let U be the subspace of R2 defined by U = {(x1, x2, x3, x4, x5) R5 | x1 = 3x2 and x3 = 7x4} Find a basis of U. What is its dimension? Collections: Mathematics