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test1-M340L-Fall2006-wSoln

test1-M340L-Fall2006-wSoln - Test 1 M 340L(60040 Fall 2006...

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Unformatted text preview: Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 (-- Name: UT EID: H C O ’U r:- £3 0 O B "O :1 n CD A 00—4 I 01M 1 009—4 V A #0::ka v Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 2 2. (10 pts) Suppose the set of solutions of a certain system of linear equations can be described as $1 = 5 + 4x3, 272 = —2 —— 7mg. Parametrize this set of solutions as a line in R3 using vector ( . notation. sq : 5+ “9 71>; ‘ 9C1 = ‘ 2 - 79¢? - it‘\ ‘ 5 + H ‘ LL / 5 x: xii-2‘ ~a~7t z Jf“".7 + ‘2 feiR at3/ t l o ) Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 3 MM 3. (10 pts) Find an equation involving 9, h, and k that makes this augmented matrix correspond to a consistent system: 1 —4 7 g 0 3 —5 h —2 5 —9 k ”i «+9 7 3 “i x -—\L ‘7 § "3* [a 3 ~55 k m 0 3 ~-5 : k 0 ~—3 r5 3ka Rg’vZH?‘ 0 0 O ~k+ugi+k $4M ‘i‘ew W'Iwmwuwg WMW E 0/9an Fig wk mi? “\T \n—e Sig-k i2. 3 O. Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 4 W 4. (10 pts) Consider the following system of equations: {327+4y 2 k . II II x+hy Determine all possible combinations of values of h and [C such that the above system has a) no solutions. b) unique solution. c) more than one solution. 3 LL 3 l k k K \ k k N O 4~3k 2-“3k RI—3R2_ La.) ND Wham ll 4'3h20 W §r~3h%0. Le. x»: Lé/g M K79 P73_ do) Thu wKuiXKm VS “#0;an Tl: Ll,_3k?:03 {Hen k¢ 4/3 @) WBWMW Wig LK'Bh’iC) W augkao) 1:9, k: LL/3 QM \Q:2/g‘ (. Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 5. (10 pts) Let 1 ——2 4 a1 = 4 , a2 = —3 , b = 1 . —2 7 h Find all value(s) of h such that b lies in the plane spanned by a1 and a2? \W) we, Wow?” dfie ,SLEMWX WW Nam 0-500 \ACC WQ‘MW CfiL/KAvw Wt u 3 ~2 KL s *1 Li 0 ~3 '\ ~ ’3‘ ‘5 “"3 RV“ ~21 7 k L0 3 we gleam : “'2 Vt ( o : ~37 E411 Test 1 M 340L (60040) Fall 2006 Friday, September 22, 2006 6. (10 pts) If b aé 0, can the set of solutions of A - x zigcontain the origin? Explain. \> _\ A .3 i Nb S¥WAU;O, UmM‘mmW ——END—~ ...
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