{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2331_test1_B_key

# 2331_test1_B_key - Lima" Aigebm 233 Tesi I B Page 1 of8...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lima!" Aigebm 233'} Tesi I - B Page 1 of8 Math 2331 Linear Algebra Test 1 — Vergion B K Last Name w First Name Peoplasoft ID# 0 N0 calculator. 0 No notes or books. 0 Work in the space: provided. Show your work naatly for pogsible partial credit. 0 Box your answers. 1 2 M12 points) Let u 2 O and v: I ; 2 2 \$3“ 2 71 5 + 2 , x. a) u v G Tl f ' i {cs 1 K L b)u-v: \wlfogx +2v1 :1: Q» 0) Length ofuz “a”: \/ 322‘. 02‘ + 17'” 5 \1 I; (1) Let 6* be the angle between 21 and v. 005(6) 2 ' ~ “MW 1"+\1~r 11’ : 3 Linear Aigebra 233 1 Tee? I — B 2 MS e) Give a veeter peapendieiilar :9 v: I l a.» f) Give a lineayeembinaiien of u 33d v that equais; w 1a+\$vz w“ 2. (10 peims) True or False? .M \ mm if a diagonal matrix does not have any zeros on the diagonal, then it is invembie. M L_ ifbeth AB and BA are defined, then A and 8 mustbe square matrices. E if AB: 8 , then A z I. \ If A is invertible, then Ax : b has a unique Solution for any I) . X:_W if A is a Symmetric matrix, then AA? 2 l . _ a k: __ The inverse Ufa lewer trianguiar matrix is an upper trianguiar matrix. Matrix A i3 3X5, matrix B is 3x5, matrix C is 5X2 and matrix D is 5214‘ True or False? _ F: AC+ AD is deﬁﬂed. W A__ (A +8)C is deﬁned. l DTC is deﬁned. l The size of CTD is 2x4. Linear Aigebra 2331 Tea: 1 « B Page 3 018 3. (15 pointy} Given the mztriccg below: 1 5 ~2 —4 2 ’ —2 1 g: D: x: o 2 0 —1 2 ~1 ~ \ a W\ O a) 148+Al): “f :2 a i G 1:; A ‘55 2“; C) i .w VM 1» ‘ 3: (All :: A W , i, i I; \C} 0 t3 0 V; m I \ ‘ UH u c) DTx: Wq O ‘ Z: . Linear Mg,ch 233i T33; i — B Page 4 €fo 4. {'20 points) Soive the tbiiewing sysicm by eéiminatia’m and bagii subsiiiuiion. x+4ygz=§5 i q: Wi V ii; 2x+10y+2244 2 is 5; LE 3.x“ + 8}; + 2: Z 39 rﬂgﬁxfﬁzalx K LE 4 M 16 2 3 “k ,w312_\+2?9“5)§23 O ~L‘r 5 we W“ W My 1‘3 g11+i1~yé9~3 \ UV 0 @ H 9—1 29.. H :: 12 2:? a: W a :W ‘3? 9*:53‘5 7 Linear Algebé‘a 2331 Test % « B Page 5 OfS 5. ( l 5 points) Given the matrix: “ :L. ’35 E“: 2x 2 I: i: u \q \o :01 Q :: L,— “M 3 M R 9 1 3] b) Factor A into A = LDU (in this version both L and U have 1'8 011 the diagonal and D is a diagonal} matrix.) A: ngwfi‘fm 5W3} 91%} ii” i Linear Algebra 233} 7631 l - B Page 6 GFS 6‘ {110 peinis) Answer the fbiiewing quasiions wit% the given mairices: [U 0 1} 51 0 \$11, 5; c“ g; g? Jr {ask P: e 2 0I 2;: I at 2 a! e f L} G QJ 4 O 15 kg i? i_ ? Seﬁ’f‘ﬁﬁ («Viki idé a) R 2 02 g {11 1 gig??? 53%;? M3“; 13‘) PA: ? a”; a“ {3: 2:? {LL 7 "M _ x "i C) pl: W C) Q i :P W *2} E, “2:; k i a“; j \ m ’3 d) 13': i x 5:: «:3 g i Linear Aigebra 2331 7. (20 points) TCSi i ~ B Pagé‘: 7 ()f8 21) Find {he inverse 0f the Foliowing matrix using eiiminaiion. } 0 ~11 A: ——; 2 ; 1 4 i \2‘1 4; 22 m1) Q3?“ ‘i {2; leﬂ +g3'e I?” «w 2mm 9. 3 ‘1 C} C; ﬁgfgvﬁﬁé {M1 Q h) Solve the equation: , «5 ‘ 2% x 2* @ «era 45:; X W £52, g g {3 w: i ‘3 ‘3 ME a % £7} 2 ":3 1 L;- E {:2 {:3 f C“) w i 1 {'2 :3». {L} f E C} q» % m i <3 i <3 - E 2 <3 {:2 1 w? H“ :1 <2 i : <3 M g‘3 #332? Q :2. *7; Q i “E? ' r ' “M M > 5 g Q a; “Aw? w%>i/a ~4 *9, 4 f; a m V I h A 2 z , w Egg/aw 2/3“ Egg, ’5‘ 2, 9?} 1 0 4 x 0 ~l 2 I y x 2 (Him: This is an equation of the form ASE-:5) 1 4 1 z 0 i “3? ~43 “’~ ., i X “:3 3A 19 m ’~‘““ “3 v: i/Z/ "f g r , , W ~ % N i L: ’k g ﬁx 5 ’3‘ W, i [A 55/ ’1} g M; W2» / 1 if; L, iv 1} L» f“ Linear Aigcbra 233i T635: 1 - B Page 8 03'" 8 Bonus {5 points) If A, B are square matrices of the same 51.20., prove that (518)” : B"A ”'. w: (3513") i5va :5 mggfﬁﬁ : g: 3: 342% ‘ \$11 {awﬁim :1 g’imwg : .1 9: r'Ef‘E v: A (iii i; :::’7 gmié (5 points) Let A be a symmetric mgtrix and comider the LDU decomposition of A . I O O I O 0 Iszl I O and I): 0 2 0 ,WhatisA? 0 2 1 O 0 DJ A "2:5 53;?ﬂﬁ’ééﬁ‘é‘iw ~53? 3'? 3: EM W“ v; ‘ “(3% W 233%» ...
View Full Document

{[ snackBarMessage ]}