Short Exam 1 14-15 Spring.pdf - METU NCC LINEAR ALGEBRA...

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Unformatted text preview: METU - NCC LINEAR ALGEBRA SHORT EXAM 1 Code : MAT 260 Last Name: AcadYeari 2014-2015 Name ' Semester I SPRING Student #I Date : 17.03.2014 Signatilic : Time I 12:30 3 QUESTIONS ON 2 PAGES Duration - 05 min TOTAL 10 POINTS 1. (319113) Let E— — {(1, 2, 3, —1),( (,1 0,2,1),,(11.,1,1)} Show that E IS linearly independent. l(i:£:3,-i)+)0,®,1,i) + &(I,1,I,I ()1: +34)”; =0 “91, + 9 :0 3} +35 +19 5'0 JHJV +y+93'oll'fl}:oy 9‘30) j/VZ/O 2.(3pts) Let S = {a, b, c}, V = Fun(S) and E = {2Xa+3Xb“Xc: 2Xa+Xb+3Xca 2Xa+2Xb+Xc}' Find a linearly independent subset of E. (2)3}hl) 3. (31.93.))<°L)‘21l)- .3-(3253,-~I) +33 (we) +53 (23%?) :0. Cay-33.361901}; . 1, 3, 3:: : e 3 =3 ~0 «33::- , ,3), +3r-k923fl. ‘£),9.¢O:28:’azj' lye) . (333m) 3 (3,132») .2. 333mm) U“ (£310, 4-“ 343—3: Xmi‘fibtifllag c/‘K'S‘ g +£‘4r.-0 X911”... ‘3‘)“.53 9:5; (SJ-leg 3“"? j ‘1‘ :«efr tax-i»? 5m :2 J 3. (4pm) Let V = 733(R) be the vector space of all polynomials of their degrees at most 3, and let U = {a0 + alx + (12532 + (132:3 E V : a0 + a1 —.— 2c2 — a3 = O} E V be the subspace. Find a linearly independent subset E of vectors from U such that Span(E) = U. 1. —-a , J. # I ) “'- a—Q 5 z ”I 3' ”’3‘! 5'" I' {Goiqwahe} “ it? ’ rflqe .. F a a. a, I!“ a "_:__ “3 W J21, §\§.53 V) é~ 3?‘ J! ...
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