math 208 exam 2 sample problems summer 2008 on linear algebra - Math 208 Study Guide for Exam 2 Summer 2008 1 Find the characteristic equation

# Math 208 exam 2 sample problems summer 2008 on linear algebra

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Math 208 Study Guide for Exam 2 Summer 2008 1)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 2and 3. 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. 4.1 4.2 3) Know how to test for a subspace. Subspaces of 2 and 3 . Subspaces of , , and m n n n M M . Subspaces of functions, intersection of subspaces. All appropriate HW problems. 4.3 #26 4) 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 #29 5) 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.