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midterm - 100000074428 DEN Homework Email To: denhw@usc.edu...

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Unformatted text preview: 100000074428 DEN Homework Email To: denhw@usc.edu From: patawaranl ferze Email: fpatawar@gmail.com Student |D#: fpatawar Course Number: EE441 20071 Day Phone: 8183937643 Company: JPL Complete this form using BLACK ink or DARK pencil only. (Nothing else faxes cleanly.) A way to test how well an assignment will fax is to photocopy it. If it doesn't photocopy well. it will not fax well. Make sure the course number and your name appears on each page of the assignment. ASSIGNMENT TITLE: SPECIAL INSTRUCTIONS: 1 00000074428 Powered by Reportée® www.reportee.oorn© 2002 Call-Tell, LLC. Reportée® and the Reportée logo are copyrights and/or trademarks of Call-Tell, LLC. All rights reserved. Patents pending. EE441 Spring 2007 4; Dr. E. A. Jonckheere Midterm Exam THH 101; Tuesday, March 06. 2007; 3:30 p.m.—4:50 pm. Name (LAST, first, 1niddle):fL+Mm,__.rE—mail address: MAI/.6‘om th‘ZC Do. Isyues o For privacy reasons, I no longer ask your SSN as extra ID, but PLEASE WRITE YOUR NAME LEGIBLY in the following order: Last, First, Middle, as they appear on your school record. 0 OPEN BOOK, OPEN NOTES, subject to the following restrictions: — Only book allowed: Gilbert Strang, Linear Algebra and its Applications, Thomson Brooks/ Cole — Notes allowed: Lectures notes, handouts, notes available through the blackboard, homework solutions drafted by grader, student’s graded homeworks, and student’s personal notes. — Typed notes prepared in a “study group” are allowed, provided they be signed by the student, along with a declaration that they were prepared in a “study group,” in which the student had a “significant contribution.” 0 Pocket calculators are NOT allowed. 0 PLACE YOUR FINAL ANSWERS AND SHOW ALL WORK ON THIS EXAM PAPER. Use extra 8%” x 11” sheets as necessary. 0 As a reminder, University policy is zero tolerance for cheating in exams. - - - = - 5.4 SUBSPACE OR NO SUBSPACE 2 - 6 HOUSEHOLDER TRANSFORMATION 5 Problem 1. LAN CANONIC FORM. 2 2 2 A: —4 —4 —12 —2 —2 —6 Consider the following matrix: 1.1 Perform the LAN factorization. List L, N , and U. What is the rank of the matrix? 0 O 1 l 1 a o U I o][-‘/ ~¥ 4;] [O D] 0 ’ ’l - *6 } l/I‘xr -e.y._. extra space for 1.1 1.2 Find L‘1 and N‘l. [_"2(£1L/)-7? 1’; 1.3 Using your LAN factorization, find a basis for the column space of A and a basis for the nullspace of A. C(A):¢(M,) , I 030 M:‘L 1'30 “l ij( Problem 2. LINEAR SYSTEM OF EQUATIONS. Given the following system of equations: 1 1 0 0 1 2 1 1 13 0 as: 2 141 3 1 5 0 4 Does a solution exist? If so, determine how many solutions exist and find them all. I l I 3 H4 y Problem 3. FIELD THEORY. Consider the set {10 + q\/§ : p, q E Q} (Q is the set of rational numbers). Is this set a field? If so, provide a proof. If not, show Where it fails. (Hint: Can (p—+—q\/§)‘1 2 ac +y\/§ be solved for ac,y E Q .9) (,m 2‘ W.)[:(/0*+¢ilyf) (p3 ;¢5£)] 1317f, +2,I’2}(/’z!2fl3)]/g§¢) ,‘iffic Unc’c/ Vb" i W / (W € 2 I firmly {Ni/i)! j / We,“ 2 "D 77 ' . sz‘ Problem 4. INVERSE OVER A FINITE FIELD. Over GF(3)7 find the inverse of the following matrix: «f ——3 -l o 9 1 1 o ' l fl u 1 A h [ 2 2 ] " l 'l A’=[ .1 _L\_,__ l 0J(J.)~(l)(0 ‘f -1 I -/-I MoJ(—]j 2 1 V‘Ioc’(-lj :/ “641(9) 2):, m) N /Z Problem 5. SUBSPACE OR NO SUBSPACE. For each of the following subsets S.- of R3, tell whether or not 5.- is a subspace of R3. If it is a subspace, give its dimension. If not, show how one of the vector space requirements fails. In all cases, :3 E 1R3. 5.1 51 ={zvz 2131— $2 = x3 and x1 + 3132 = 2x3}. 5.2 52 = {x : $§+x§ =x§} 5.3 S3 ={1I321I31IE3 = 5.4 S4 ={zv 2131+ 2132 +133 = 4} f . 7 1- a 1/5 3 ../ 7) 6:0 ywb €5,5p 5 S j/dc€/ Ann 3; S‘.L Q l l a )(31 .1. Hz — xi“; «1 “‘1 ()(1 + D 0 ~ //1 A “ ,L K c. >1 ; +>/,>(3 +11%} V J O / / x :a / l “9" Jugs/“(Y n. 71' (ALA/17$, (fol/SAW? Problem 6. HOUSEHOLDER TRANSFORMATION. Find the Householder matrix H such that: END OF EXAM ...
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This note was uploaded on 09/11/2008 for the course EE 441 taught by Professor Neely during the Spring '08 term at USC.

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midterm - 100000074428 DEN Homework Email To: denhw@usc.edu...

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