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Math 208 Study Guide for Exam 2 Summer 20081)Find the characteristic equation, eigenvalues, & eigenvectors given an mxn matrix A.Look at the T/F questions.3.42)Write a given vector as a linear combination of other vectors in 2ﾡand 3ﾡ. Know the definition of a vector space and the summary of important vector spaces. Determine whether a given set with the standard operations is a vector space or not by verifying the 10 axioms.4.14.23)Know how to test for a subspace. Subspaces of 2ﾡand 3ﾡ. Subspaces of ,,and m nn nMM. Subspaces of functions, intersection of subspaces. All appropriate HW problems.4.3#264)Definition of span and spanning set. Know Thm. 4.7. Definition of and test for Linear Dependence and Linear Independence. Thm 4.8 and its Corollary.4.4#295)Definition of basis and uniqueness of representation (Thm. 4.9) Know Thm. 4.10 & 4.11. Definition of dimension of a vector space. Thm. 4.12. An important section, know how to do the HW problems.