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Midterm 2 Review

Midterm 2 Review - Math 5A Midterm 2 Review Problems Linear...

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Math 5A - Midterm 2 Review Problems - Linear Algebra Winter 2009 The exam will focus on topics from Section 3.6 and Chapter 5 of the text, although you may need to know additional material from Chapter 3 (covered in 3C) or from Chapter 4 (covered earlier this quarter). Below is an outline of the key topics and sample problems of the type you may be asked on the test. Many are similar to homework problems you have done–just remember that you will be required to show your work and/or justify your answers on the exam. 3.6: Span, Linear (In)dependence, Basis, Dimension. 1. Determine if each list of vectors is linearly dependent or independent. Justify your answers. (a) (1 , 2) , (2 , 1) (b) (2 , - 2) , ( - 2 , 2) (c) (1 , 2 , 1) , (1 , 3 , 1) , (0 , - 1 , 0) (d) (1 , 0 , 0) , (1 , 1 , 0) , (1 , 1 , 1) (e) x + 1 , x 2 + 2 x, x 2 - 2 in the vector space P 2 of polynomials of degree less than or equal to 2. 2. For each part of Problem 1, find a basis for the span of the listed vectors. What is the dimension of the span in each case? Justify your answers.
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