MA 262: 4.4-4.5 Review- Bases & Dimensions of Vector Spaces, Row & Column Spaces

Review of lesson 4.4-4.5 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 4.4 covers bases and dimensions of vector spaces, including the definition(s) of a basis of a vector space, the standard basis of R^n, finite vs. infinite dimensionals, and relationships between bases, span, linear independence, and number of vectors in a set. Delineates procedure to obtain the basis for the solution space of a homogeneous linear system. 4.5 covers row and column spaces, including definitions, row and column rank (and relationship between these), determination of row equivalence, procedures to yield both row and column rank, and connections to the calculation of bases of subspaces. Also reviews how to obtain dimension of null space given row/column rank. Example questions included throughout for common styles of basis exam questions.