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McL 151 Assign 3 KEY

McL 151 Assign 3 KEY - ’ ‘ Y SCORE £25 NAME K5 STUDENT...

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Unformatted text preview: ’ ‘ Y SCORE: £25 NAME: K5 STUDENT NUMBER: Math 151 A03 & A04 Assignment #3 DUE: WEDNESDAY MARCH 10"“ 2010 At the START 01f CLASS ~ NO EXCEPTIONS! *** UNSTAPLED ASSIGNMENTS WILL NOT BE ACCEPT ED*** ANSWERS ALONE WILL EARN YOU NO CREDIT. ALL RELEVANT WORKINGS MUST BE SHOWN IN FULL. COMPLETE EACH QUESTION AS IF YOU WERE PRESEN! ING YOUR SOLUTION IN THE CONTEXT of an EXAM. ______________________________________________________________________________________________________________________________ 1. Solve the following system using Gauss-Jordan Elimination. [5 Marks] 3x1+ 2x2 + 12x3 + 2x4 + 15x5 + 14x6 = 13 2x1 + x2 + 7x3 + x4 + 9165 + 8x6 : 7 L. glyigcg llﬁ’lééé— Z ’Z ’7“ ’5 ”r ’5 HQ 0:32378 3 £_m ,, , _ -» I f; 3 l l a. 3 7 __‘____+ O | 3 ad 5— in? ,2 2 (Z 3 Mr {S 15 KKK? 2 2 m 3 :LE— *5' [5 95’4““ 00913 3 5 ’ 2 (2 x I *- 2-!1-—-t-2 . *0 lGZ-lliZ1 30 . Wrak’ ﬂ 2 (“K2 ' ‘ 121—2163 {31 34'} 1 l 2 l.“_'.nn_ﬁj_> Jl :3 9 l l “we 0:32578’ .u,,___ﬂ_> I2?}3!‘, 003;? : o o o i .2 3 3_ 00 0 d} PC. +- 2713 rt Big “T 939% “-l Xgﬂ'f 3:2(3 wk :15" +3145: 1" Z U?.'§'ZDC§"\'33(L:3 ' Ff‘ v.4: Tmﬁu‘mngrwlz N\.l7'.m."uu:x 3:?tzuv'z516'H-‘w‘ P2 ‘— x%:'5‘21f“3xc \ pg" lﬂZf"“F 9% xx: 2-31-5“Xy~x& 7(2’2’5rf*ﬂ A 91L? y 5. 2‘34? ‘4; 1:5 3(3—26 N5, - ,6 j I)”: ff «4, 1/15.? “/3 C K X5 k A A, B and C are matrices defined as follows: —1 1 1 3 1 2 3 A: B: 0 —~1 = 2 1 1 3 5 1 0 QxS 5K2 a) Solve the following matrix equation for the matrix D. [2 Marks] 1 AB - —CD = 0 2 “Zap: — (A13) 42' c 13 —— A s (f D ‘5 2 A?) 35‘ ; C"(‘2AE>} FrewflGLr—o‘i C"f aim-EV b) What size is matrix D? {1 Mark] 47x 2 WLIF‘UK ff ”Jammie. mil-n7. at?) starc. 43- c) Find the inverse of C using the method which can be used to find the inverse of any non— singular square matrix. [3 Marks} -. I T23- 312T 2 "mm“? ca I 0 r l [2 3\15 Kerk: [“l*7- ,. 5—: mg; I Z ha» 6 l [3 5‘ 7) 5'” d) Find matrix D. [2 Marks] E l 3. Deﬁne matrices X and T as follows: 0.6 0.3 0.1 x=[xI x2 x3] T: 0.4 0.3 0.3 0.3 0.3 0.4 You will find the values of x1, x2, x3 which satisfy X = XT and x1 + x2 + x3 = 1 through the following steps: a) From the matrix equation X = XT, find three linear equations involving x1, x2, x3. [3 Marks] w. M a. "1 i" C“ ' 3’ ' L t 1 = l l L»; a! ; .cx, + .v x. 4 ,. 3361:. xx :- .3x, + .339“ + . an. 22:33 ¢l9([+'39(—2+'Lt3(3_ b) Your three equations in part (a) above, plus the equation x1 + x2 + x3 = 1 together form a system of four equations. Solve this system for x1, x2, x3 using the Gauss— Jordan elimination method. [4 Marks] a ' 1 WE 11+x2+xali {ii I ’i i iii 42c 43! 5% r0. i 4 ~ir' -? oigzt’lﬁjWOﬂ’t‘Z'HGi « l'”- 1" ~3“ ' ' W §——-> — i=0 “'5xi’r-7z'-5 a" _1ﬁ_,5 {0E0 mastic malUCI ”-31%; +.¢x3=0~ - ._ l t i l i E K H i I K 2’}? \$10 —3 *Is ‘ ~r-G 5” 0 4W” 04.4?» 0 ‘ 3 ’ ﬁt+,’,°..§‘ (f) 0 o O a J o-.2.'? ' ~33 2 0"2'7 J K’JrR; 0"2'7‘ @000 one 0 ’9‘ _, 2-“. fr 337g 127/"3r 1: -. K/ .-i r“ i I i i 1 0 ~’ , ‘1: 13/153 i I i i _—__L K \$1.55'ifk Qz+~sr533 Ci 0 3/30 RI le‘ici /Q.» ‘ , -3“? AI 5.0" 5 )1 2; . 8/2.. J .. l a K);"’Qa 0 8M? > 00 I 3.5 Kiwi”; 30‘ H wooao _-._.,,..M..ws.-..y. O ‘2) "35 ' "7;: £3 C: o o g ”’ G a o 0 0 f} 3’) .2. if - C" ‘ 1t+12+1\$2l .77 M?E+IO-+S§¢l Suppose some experiment has events A, B, and C, and that: i) P(B) :04 ii) P(C) :05 iii) P(A|B) = 0.25 iv) P(B|C) = 0.5 v) P(A|C) = 04 vi) P(AUB) = 0.6 vii) P(A mg no) a 0.05 Find the probability that exactly one of A, B or C occurs. [5 Marks} .05. :05? .05)“ ”i ________m_ﬂitﬁw_mw, m— .V ,. ,iS ' 2 Ppﬂ — ,3 (’Ftwwim Q) i N5) , Mr (emit) C mm 3 .20 (RNA f’ " ‘ ; .2: “PU/re 4ch = .03" (cam) [ @353 >W __ _ c P(A U 8 r . Q, 13 A18 2.2: O | , ( > r? with tie) ”Pimeﬁt g; 19(A/i.b,i:.25 Wﬂmqw-mmé F05) - WA) u 3 Poi/1630 25 "*2; " @ 7% A [(5 r H rug/Us); ii :7 {fa—lie} : #0 ”H55 [9(BiC): a5— ngi/Ei‘): Li 1-? 1°(E/ic3 “5 (M5)” 2 We) P MM - sharia.) , 5 ...
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