Short Exam 2 16-17 Fall.pdf - METU NCC LINEAR ALGEBRA SHORT...

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Unformatted text preview: METU - NCC LINEAR ALGEBRA SHORT EXAM 2 Code I MAT 260 Last Name: AcadYeari 2016-201 7 Name 1 Semester iFall Student # : Date 226.12.2016 Signature : Time I 18:40 TOTAL 11 POINTS Duration 340 min 1. (6} 2. (5) 1 ‘ . l ‘ I Ilgm-i ¢ 1 i l J Show your work and justify all your answers! 1. (639) Let P : R3 ——> 1R3 be the skew projection of R3 onto the plane H= {(rc,y,z) l sv+y+z= 0} parallel to the vector v = (0,0,1). Find the matrix Mg (P) of the projection P relative to standard basis E. A basis BTT ”For ‘H/w, Plane 7T : B11:{V1:(1)“4,0)JV1:(C51I—1)E :bP is 421(31th J05 I PCV1-i 2V1 FCV1):V9_ PCVI): O 'Févr M:CF\ "we ShOUlcl CO.MPLti€ POE/1i, P(€1)} H83) in ‘Hqc 35"}thde [305 3° : e1=(1‘o,0\=(4,-4',0)+L0, 4,-4)+(O,D,4): v1+ v1 iv e; 2(014,0)=LQ11~1\+(0:014) : 1+v eg:L0,0,4) 2v PC63- )3PCV1'PV) : PCVQ +P(V) 2 V2, :: (0 11,4) 1 i i l $13091} : W v1.+vl+v) : PCv1)+)3(v1)+'PCv]_-_v1+v;: (410,4) i I Pregan :0 :(OOO) METU - NCC LINEAR ALGEBRA SHORT EXAM 2 Code i MAT 260 Last Name: AcadYearl 2016-201 7 Name 1 Semester 1 Fall Student # : Date 1 26.12.2016 Signature : . Time 1 18540 Duration 140 mm TOTAL 11 POINTS 1. (a) 2. (a: a l I I III“.- '_.'.. ~— A lawm- Show your work and justify all your answers! 1. (639) Let P : R3 —> R3 be the skew projection of R3 onto the plane H={(m,y,z)|m+y+z=0} parallel to the vector v = (0,0,1). Find the matrix ME(P) of the projection P relative to standard basis E. Hg gzolu‘l'lon: a chz is A nullyfl 5 {M We 871:;{V1z(lflplfiflglpfl? 00] l O o 0" WM le‘vtflxflf saMgPl: MEWlMEWlM? (M t Pt V1] 3 V2. :19le; (:16.le b3 Pqulzw ma M:(P):[ Pad—TO (30—; M: : 61 5(1qu =Vl+vl+v g 1 09 6L:(O,110\:V1+V HELL”: J); ’l 1 5% ZLQOA): V 1 E 10 O 10 O 10 O :l. O O awmzwo om 1103010 b 0—11 0 O O l l ’l ”1’1 0 2. (5p) Find the solution set (general solution) to the non-homogeneous linear system in R3. 33—y+4z=3 33—2y+7z=4 A 3]~ 5: “l 3 Rz+(*1l21 "4 #4 L: 3 I: 1 Q—_; i"; 3 R3+C~4).lz1 O 3 ‘9 “3 - 4 w 0 *1 3 ’1 4‘73"" R2. __._.____~3 O 1 -3 "/1 “M3 0 1 “3 __,( R3 +(+%)XRL O O O O O O O O .=‘t> X+ 2:2 } ng‘a} \. ?CLr'chlar S‘OlU'Il‘lo’L 2:: O “I? M", 2(2-4 0, (pl-fl? {Ear- mid-anon %:1”‘4’ W0=(1+Q ’0 25 GU10 H42? Pwlxculm so! > W gjjgi E {CE/+3232)! 2612 } :psoLhoffii—ism lam Gen} :Eiolul‘lofl Se/l‘ _-_—_-J{(2 ‘1 O} +C (H1134) ...
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