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Unformatted text preview: MATH 262 Spring 2010 Practice Problems for Midterm I There are 20 multiple choice problems and 1 handgraded problem: 1 handgraded problem is a mixing problem! Problems you must study (1) Example 1.4.6 in page 38, # 24 in page 41, #3,5,6 in page 39 (Not in TrueFalse review) (2) Example 1.5.1 in page 42, #1, 2 in page 42, # 1,2 in page 47 (Not in TrueFalse) (3) Examples in page 5053, #15 in page 55 (4) Example 1.7.1 in page 58, #3,4 in page 65 (5) Examples 1.8.6, 1.8.9 in page 6974, #24, 25 in page 76, #37,41 in page 76 (6) Example 1.9.6 in page 83, 1.9.7 in page 84, #11 in page 89 (7) Example 1.11.1, 1.11.2 in page 99 101, #1,10,14 in page 103 (8) Section 2.5 is extremely important. #21,22,23 in page 160 (9) #24,33,34,36,38 in page 210211 (10) Theorem 3.3.7, #10,15 in page 222 (11) Go over all problems from quiz and homework Study guide for Exam II There are 22 multiple choice problems. Exam II covers up to 6.2 (1) Go over Exam I: there will be 5 problems from Exam I after minor changes (2) Go over all problems for homework and quizzes. (3) In 4.2, you need to know definition of a vector space and properties given in Theorem 4.2.6. Use them to determine whether a given set is a vector space or not: Problems 6, 12,16. (4) In 4.3, you need to know definition of a subspace: Problems 3, 5,8, 18. (5) In 4.4, you need to know a spanning set, a linear combination: Example 4.4.9, 4.4.11, Problems 4, 9, 12, 14, 22. (6) In 4.5, you need to understand LI , LD, Wronskian: Problems 4,9,13,32. (7) In 4.6, Need to find a basis for a vector space and determine the dimension: Problems 6,11,17,23. (8) In 4.8, You need to find several ways to find a basis for colspace(A), rowspace(A).Look at Examples in this file: Problems 8, 12. (9) In 5.1, need to know definition of a linear transformation and determine whether a given may is linear or not: Problems 4, 8, 10, 15, 27, 30. (10) In 5.3, Given a linear transformation T , you need to find a basis for Ker L , Rang( T ), and their dimensions: Problems 1, 3. (11) In 5.6, find eigenvalues and eigenvectors and need to understand meanings of them. You need to be an expert on this. If you get a wrong eigenvalue λ , then you will end up with having a zero vector as an eigenvector corresponding to λ , which is totally wrong. Eigenvector is never zero!!!!!!!!: Problems 5, 7, 20.never zero!...
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 Spring '10
 JinHaePark
 Linear Algebra, basis

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