343_Final_Solutions - MAT 343 Final Question 1 A is a 3X3 matrix det(A = 2 what is det(5A equal to)d(gAl AokigcJAl HIM $630M wk CAA Aeneid HM AW

343_Final_Solutions - MAT 343 Final Question 1 A is a 3X3...

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Unformatted text preview: MAT 343 Final Question 1 A is a 3X3 matrix, det(A) = 2, what is det(5A) equal to? )d-(gAl ; AokigcJAl , HIM) $630M wk“; CAA) Aeneid) HM AW toluvvwx 9‘; A; J“ Lem? wwll'Iin/um t («cl/x 0‘; HM "é Sis (Mme Out In flu ‘Qiuestim* H “a?“ Jei‘gAl‘gum ”it __ Find the eigenvalues and eigenvectors of the following matrix: _ ' -1'A (, A=( 62 g) iA "\I’Li : i t V-Ai :-(1+)l(1..f\)-24 = - u. -s‘A Mist —. A1-s/\-§‘o :(A—IolUH) Sn Aflo s)\ /\Z.—'§ ‘ A1 1 Axl)‘;10 0 AX:I\KIA:’I’ ...____________._.____.--—- _ (A—NII\1L:0 _____ . _ , ( " ‘11 J B QuestiOINfLN ~1iml(::):° (ASH: TX") Compute the following detenninalnt:'---.__‘ (-n é)(x,] 0. 1+; 73; " J 1 2 3 l ‘ --'> M “° 6 x .1+1I'}| 3 143 I ’L 31 0 1 2 lunx‘ +6X :0 (3 X ()10 (A Lo. 1 1 4(a) 1 .94 -_1 4 —1 1 l “V e .1 “t h i I A”! ': txt,‘$1¢:o 151.4653“ 1 l 3| 1 a 1] i “1113‘. l61|+l1xqto Lo | '- LI -1 t _ I (“kin-L, up-” 1 ' l l'l'L -l('|,8) I U :(.) uLLXZI ’0 2-J F ’L Hfl i "" ‘7‘ =".1__ ~ll-1(J}l,-H+'? L; ; V ,Tl l .1 may (I ..—._ _ _..—_ Question 4 If Au] = Alul and Auz = Agug, if x = 3m + 4112, What is An: equal to? Is a: an eigenvector of A? If so, for what eigenvalue? _ "—“fl AX: AIBU‘+ L'Uli :. 2A0... (JAIL; :IZA‘U" + LA1U1:A)\ vxoi 9AA eifi.lwv£u\'01.'uvxill§ A,;/I1 Questlon 5 i. _ _ _ Solve the following system using Cramer’s rule: X I 2$1+5$2= (1 g (.( > o I‘L I)“ {331+4x2: (a '1‘ “ML {/JLAM A71: II '3' H to t —1 If1 I — Ill 4’";1'1:1li 71 .1 H-i-I-le L; m 31___J'% ——-I’.z il MI 3 5 L' n) Question 6 Estimate AN when N > 1 (meaning N 1s very lar)ge )if: @IA ArI- A=’(__21 21) A;1,_lf)4zi1rf (a), WAN-I; 03) w; WC 1’) m";- .TITIIJ' 7‘1) : Az-W” Question 7 _ ‘_ ‘--. A 5 Can the following matrix be diagonalized? \I"W A“: M DN M | M (c: 2%)?1-1 2 l { ~ A=<o2> : ”(I '1)(i§~)-;{.'.JI bi \ 1 ., ff»; " 0 '2,/\I (1-A\'° :"|1(‘ ')('3~ 3N) ,. N ALL mdi'i 2 ‘ i£3N |'3N>~ 1(3" -1) ‘ '7,(_n,3“ H3" is»: " -3 1M ...
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