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Unformatted text preview: 100000074428 DEN Homework Email To: [email protected] From: patawaranl ferze
Email: [email protected]
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 CallTell, LLC. Reportée® and the Reportée logo are copyrights and/or trademarks of CallTell, 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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 Spring '08
 Neely
 Linear Algebra, Matrices, Householder transformation, Alston Scott Householder

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