{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2004-2005 Spring MT1 with key

# 2004-2005 Spring MT1 with key - M E T U Department of...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: M E T U Department of Mathematics Basic Linear Algebra LMidterm ' COde : Math 260 : Acad. Year: 2004-2005 Last Name Semester 2 Spring Instructor 1 D t i 29.03.2005 Tiam: : 17:40 3 Questions on 4 Pages Duration 1 60 minutes Total 30 Points 1 1 1 \$1 1 1 1 and x = ‘2 U 1 1 333 l —1 0 0 - .- \$64: " Name 3 _- Student No I Department: Section Signature : (5+4+3 pts.) 1. Let A = l: :1) Find the conditions on a, b, c, (I such that AX = f: has a‘soiution, i.e-.I the system :1 is consistent. 4 4 4 4 . Q __ E 1 1 . 4044M) ﬁ’ﬁ 01,03xgﬂ rpm—>0, 01 ’l 1‘0 7 0 1 1 ‘c A/""-> 4 ~10 0: d “VHFWQ. o *1*1-1ld~a ’1 1 1" :q 4 1 4 1'0: 0 *1 00 ‘b'ﬂ Jug—pal 0 —-1 o o lbaa 0414.0 ”“90144’0 O ~1001d-qd-c r 0 0-0 D Id~ +C1- —lo W systm {is Longfbfmlc ”he d +C—b =0 (:7 1 b)Find all solutions of AX n {1) . Horn {"4“ a; “1.9, know ’le1‘ 00'1 411/1‘1 f‘rrqo ‘ 911\$"ng __ \0 “WV” 0—100 0 3 000 01.0 QOQOIO __—. 4 '1 “I C)? 1| Q Q 0 @(ﬁfgﬁwg #11 I 'l (O K '1 00% (1+(‘3—7F3 . o "a? H‘ 0 ll éfzﬂgﬁﬁf I. OQOIII x12‘ 40010 204’] ’o 30/ XleO 000010 nyﬁo =2) [gr-XL. Elna-s: 91 51 :1 0) Let Y = y; 22 and B = 1 1 , ﬁnd all the conditions on a, b, 6,1'311311 that :93 23 D 94 24 1 AY = B has no solution, Le. the sytem i inconsistent. U) Rom W 0i (Md b',-‘“35€e-M+W M. svﬂem Mn?) is Encorersmt when cebd. 10 —11 11' 0—110 a) Use elementary row-operation techniques to Show that A is invertible, and 11d til—1. (4+4+3 pts.) 2. Let A = 1—“th Draws-4 G "1 ”NO”! 00 “.3 014 “1 110449040 0.10 0—4’10000’1 »—1 “1010064. J ﬁ121; 44.nov, .1 . 1\\\\J .IIIIKJ 111IWA comm 0004 I 11 CL 00,0 0040 0.100 _ 4. 04.0 11.100 001.. , a .1000 _ L U004... T\|\|L 400W— 1.\|.|IIJ q|lJ U040 3 2 0.14.0 .1... 010.0 I «he a 4.41M. 1O ﬁooow ,. E .110. 4.1 k [I‘l‘L 7“. Tu} will; _, ..L_, s rw. ””0404 0004 0004 ..|.MH.IJ X @rﬂﬂwvﬁ MOOAso 04.40 4.04.0 MMNMDOW J! mOAtOO 0400 01.00 __ FIIIIIL Illltd. mWOOﬁ 43000 E q A 2:124 .w : VI]. : A vm /. /I_I w ES 2 n... m 4.440 m Que E m 414.1 m all m , , . .I m will}J WIIIJWJ 9. mmmm SUMO m 0001 0601 0001 00.“ mmnm0100 I .1: m. 004.0 004:0 004.0 00»... 001.0 000,, m 0490 0410 0101 0400 h rail. @940 m 1646 1000 4000 00 m X 1,400 m a, z a Jan 1.000 Cum]. .6 E (3+4 pts.) 3. Use the properties of the determinant function to cbmpute the following determinants over R. 89 88 88 37 ..,[‘I1f1_)m 1 1 21 F‘— a) Compute det(A), ifA= [2: Z: :2 S: . n 1 1 11 2 if”? % % m w ‘73*ﬁfﬂj 4 1 1 I O 0 1 O ' “*7 o O o ’1 8685 34 J; ’1‘ A P MUG U56. [Ckv' Opel-awn!) m‘ ML _ '1LjP-C cﬂ‘ «(5 ~53 Serz... M, 1% 0p. er m: (ﬁcve NM? 606% eﬁécr m; M «em-ammr M; M? (3112+ A: (16113 .. 0 0 1 oleﬁb: \$101 1‘ ’f H 1 : Sea-36:4 @685 83 3635“ 2 d y 4 2d 2y b) Giventhat det(l:a —1 z:l)=4,con1putedet([—a+Qy 1+dy —z+y2]]. b :c 1 b—2 m—d 1—3; A . . E: , _ A Hr? —~a 1mg ) 41113 Hm Wm?- M“? b 11 '3““1"9F3' km. X-jj 1—3 bie’rn («CF-““7 “def“ “jg? *dei‘ﬂ ”71W”? Q(*d€¥ﬁ)=d€‘fg u ’ “if" “309‘; (38%- rﬁmum W, “*2; Lu “W: 612‘ ;m, may (M ‘ '. - - c. r: (1?. (What) by OPEQ» c:.r;~»rg~~—>{3 3 H; ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern