fc108B-2011

# fc108B-2011 - MATH 108 B ADVANCE LINEAR ALGEBRA WINTER 2011...

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Unformatted text preview: MATH 108 B ADVANCE LINEAR ALGEBRA WINTER 2011 INSTRUCTOR : Gustavo Ponce (oﬀ: SH 6505) (phone : 893-8365) TEACHING ASSISTANT : Keith Thompson (oﬀ. 6431 N) SCHEDULE : 1230 pm - 150 pm. ROOM : Phelp 1260 OFFICE HOURS (instructor) : W & TH 5 pm - 630 pm. (T.A.) TH 4 pm - 5 pm. TEXTBOOK : “Linear Algebra” by S. Freidberg-A. Insel-L. Spence PROGRAM : review of Math 108A, and Chapters 4, 5, 6, and 7. EVALUATION : First Midterm (30%) Nov. 3 (5) Homeworks (30%) Label your work clearly and staple your papers together. Solutions to selected problems will be available online in my web page. Second Midterm, (40%) Dec. 1 HOMEWORK #1 (due Oct. 4 in class) from the textbook Chapter / Section / Problems : 3 / 2 / 2(f), 4(b), 5(d), 6(b) /// 3 / 3 / 3(c), 8 /// 3 / 4 / 2(b), 5 /// 4 / 2/ 10 EXTRA PROBLEMS : 1) Let V1 , V2 , ..., Vn be a ﬁnite collection of sub-spaces of the vector space E . Prove that the union of V1 , V2 , ..., Vn is a sub-space of E if and only if there exists j = 1, 2, .., n such that Vj contains all the Vk ’s, k = 1, 2, .., n. 2) Given the vectors v1 = (1, 1, 0), v2 = (0, 1, 0), v3 = (0, 0, 2), describe geometrically the following sets 3 3 B1 = {(x, y, z ) ∈ R : (x, y, z ) = αj vj , αj ≥ 0}, j =1 3 3 B2 = {(x, y, y ) ∈ R : (x, y, z ) = 3 αj vj , 0 ≤ αj , αj = 1}, j =1 j =1 3 3 3 B3 = {(x, y, z ) ∈ R : (x, y, z ) = αj vj , 0 ≤ αj , j =1 αj ≤ 1}, j =1 3 3 B4 = {(x, y, z ) ∈ R : (x, y, z ) = 3 αj = 1}. αj vj , j =1 j =1 Typeset by AMS-TEX 1 ...
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