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midterm 2d - Name ID NumberHtD‘I 2.1 1 3 5 TA Name(Rank...

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Unformatted text preview: Name: ID NumberHtD‘I 2.1 1 3] 5 TA Name: (Rank Section: Tux—s - S'ODF‘H 'cotoopH NIath 20F Exam 2. Mafia November 19, 2007 No r-a.£r"ulr:.!.m:-s' or any 01hr?" drmicrw aw allowed on. this (rm-m. I-‘L’Tiffi your .t-‘Ul'iti'ifmfi alarm}; um! Irwihly: rm art-(fit will br 9.5mm. for“ fligrfibfrr xm'ufi'ions. Rim! mob. qmrshrm. cunjufly. U (my qur-rsfiinn is nu! rhw'. rmkfu-r rrhn'rflr'afiun. Answer each question completely, and show all your work. 1. Cousidnr Llle 11'1z1.t.ri('es 1 's 1 4 2 9 ‘3 1 (1 ob 4]. . _1. “H- H' l 1 (a) (It) points} Computv tlw 1113111005 AB. mul (“1. (b) ([0 points) Find a null-Fix D mlutjon of the Illatl‘ix m111atim'l CD = I — (ABJT. F—_—‘ 2:: ".5 3K 1 = L; (Q RE [2 2 “2+3+l '2.-'5+[ W “”"‘ ‘1-2—1 1 2 3 2. Consider the matrix A = —l —3 0 . 0 —2 5 (a) (10 points) Find A“. l (b) (10 points) Find all vectors :1: solutions of the systen'l Am = b, with b = [0] . 1 O'Z M _2 3 I b b y I Z 3 \o o " 3 0 ° ‘ ° ° ”'3 'l-\ D x o -'2 S o O | _ .22 ° 7- S o 0 | g: s n o o . v. 3 . o a o o '3; -l '1 o o l -3 —. -. o (3 . ”1 '1 I o 0 l 7. 1-1 ,3 l 7. 3 I c o [O I c "5 ~ [ o 3 "=1 ‘Io *6, o '3 ( S 1—2 0 1 g S 7.;_ S ‘3 O l O 3'70 Cl 0 S g‘ ‘3 o ‘ 2 2 “I 3. Consider the matrix (a) (10 points) Find a basis for N (A). (b) (10 points) Find a basis for the Col(A). (a) I i “H —l v-I l l -H ~I ‘ 2 l | -q 2 3l ”:7 “I 4) o (P {‘5 3 c 7. 2. 2 H '9 ”I 2 H ~69 \ l 1 -Li “I O o 2 Z '/ ° 2 l I @' l 2. O Y - ' 3 X 4% O | '1 I A a) ' 6 'S ”i o O Q. a Y'i ‘5 I I .2 Y! ‘5)! _& O o o D 3 X 3 2.)qu Y “S 3 + .= _ 6 1 X5 +3.1.)(H10 Xi‘ ~X x$‘+}, )(u. EQSKS .5 S 16"“, K's‘X...‘ k _, 3/2 ‘ "/ o (,2 Cb) ? l i 7 --L (220 pointh‘) Find the" (film-2118101! illltl give a lmsis of the vm-Lrn' space. 1-". spanned by the vm't 01‘s Hi —3 1 i 'U} = I] . ’U-_ = *1 . “3 = a; . U: = 1 l U S 2 :3. (‘20 points) Let. r: : {£51. 012.03} and h = {111. b3. b;;} be [-WU imam of R3. wllitth Satisfy tllv following 1'vlnLiuu: a] = b] — b: [173 = —b| + by +311 (1;; 2 b2 + 2b“; Find the mmlmnnnts [311, of tho vorlnr a: = $50.] + 2&3 + a“. Qi: I #l D i " ‘I a1: ' a1): 1 O 0] 1|] ‘ H‘ I P | ...
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