MATH 220 Name FINAL EXAMINATION v u c oS IDecember 13 20011 ID Section There are multiple choice questions Each problem is worth 5 points Four possible answers are given for each problem only one of which is correct When you solve a problem note the letter next to the answer that you wish to give and blacken the corresponding space on the answer sheet Mark only one choice darken the circle completely you should not be able to see the letter after you have darkened the circle THE USE OF CALCULATORS DURING THE EXAMINATION IS FORBIDDEN CHECK THE EXAMINATION BOOKLET BEFORE YOU START THERE SHOULD BE PROBLEMS ON PAGES INCLUDING THIS ONE l MATH 220 FINAL EXAMINATION umLiUli 1 What is of following system of equations 2X2 X3 2XI X2 2X3 3 3X2 4 1 Xl Xl Xl 1 b Xl 1 X2 X2 is free x3 1 c Xl X2 X3 and d Xl 2X2 X3 X2 X3 and l x3 X3 l is free X2 X3 X2 X3 1 L l 0 4 X l e 2 I J are free 1 2 rJ l 1 0 1 0 r c u OA 0 Q Cl 0 J Q kIS S tV are free o q C b QV s PAGE 2 N J 1 1 0 5 Q oI o a IJ j 0 x L 2 A B f ll 2 Which of the following matrices is in echelon form but not necessarily reduced echelon form 1o 32 a b ll d 1 0 0 2 O i MATH 220 FINAL EXAMINATION 3 What geometric figure aV l f l 3 b a line A L a plane i 3 5 bed rJ As N L a A only we Led b B only 4 t clJ t3 S 0 c A and B A and C rvr Ii v C 1 o l1 Q 0 3 I 0 Ll 0 o I l db 0 3 r L 0 v q IQ 1 0 e I n CtLN WO r M A 5pClM1 EY h 1 V ectot r tQ 3 tR3 J a 0 j 5 0 0 r J w m m m SO G 0 tV J lffi 3 f Vo t 31lQ 9 to CQ U G A I A L V L t I IrI l 3 u I ck C c A I U d t k 1 h L d 0 9 4 Which of the following sets of vectors span 1R3 A W m CoL OJJ 0 0 C VVI two pl vor O olcA Y Vl1 I SO 5 u It 5 f 1iii iV v is lot Q A 4 0 A rhu Y M l V LI d J s 2 3 1 fJ e V cc tV I d VVI u A e d all of 1R3 A l m H i mformed from the span of the vectors a a pomt PAGE 3 o 2 N CD 0 0 1 1 0 3 0Ijo 50 C 5pvvn If 3 PAGE 4 FINAL EXAMINATION MATH 220 5 For what value s of h is the system with augmented matrix G G consistent It is consistent for all real h is consistent only if h c It is consistent if h 8 8 d It is never consistent 4 h 3 tr1 cd I Vy j0 Yb 0 0 N 6 Lk h K 0 Ulha J 31 LI 0 t4 l J 5 V L f M J 0 Go s h IS o oV 0 aJ Uf 1 no J fa lJ Y v k 6 Suppose A is a matrix with three rows Three of the following statements are equivalent Which statement is not equivalent to the others a The columns of A span jR3 A has exactly 3 pivots A has a pivot in each column d Ax b has a solution for all b f I r anJ c 43 c ve Jr n t c no vi fh r 0 I U VVl Vl A lCvr E jR3 u cJ e J o t Y I 0 MATH 220 FINAL EXAMINATION PAGE 5 7 If the augmented matrix of a system of linear equations has the reduced echelon form shown below 2 0 0 1 0 0000 03 OOOO 2 then what is the set of solutions of the system CD t I 0 a x b x 3 xa 1 2 0 0 0 S t x 2 0 1 t 1 2 Az t S n m t I 0 x I 0 3 2 Xl 1 0 0 0 xa 0 0 0 0 1 d x I 0 1 3 xa 2 2 0 0 0 2 iI 1 0 0 0 t X c t i X y 1 3 x X 20 x bCA s c 3 2 t t C 0 0 Hg 2 PAGE 6 FINAL EXAMINATION MATH 220 8 Find all values of h such that the set S W m nn is linearly dependent VI a 0 UJe WI fOr c 2 l 2 3 J 1 3 1 j o 1 1 1 2 A I 1 01 0 0 h J Q d XI wh c h Ilw h 2 I It J VI ha r 2 l t x 3 1 3 0 t k t v l 5 k f V V 04 b O VL J J Val ues 501Ckt Ob In II c J a r fl I 1 3 1 kin 3 t 1 1 h i 2 3 I I t 1 0 0 J U 0 1 I J OJ 0 h1 2 0 I hl 0 9 If T JR2 R2 is the linear transformation which first refiects points in the xraxis and rotates points in the counterclockwise direction through 7r 2 radians then what is the standard matrix of T a If b I c 6 6 1 I 11 e l J el l ez l j J e 2 Sea Vld evrci f Y CA y A 7 e j 1i J l MATH 220 FINAL EXAMINATION PAGE 7 lO If T is the linear transformation defined by the formula T x Ax where A 2 2 4123 then which of the following statements is true a T is one to one and onto b T is one to one but it is not onto T is not one to one but it is onto d T is neither one to one nor onto 1 A dL1 l 1 3 rW l 3 1 J J L 9 01 31 N i tree lk JI VC tAn ee k YOW rOY bIt 11 If A y T AA O s o to T t L to 0 n o l 5 1 1 1 o 1 1 001 then what is the second row of A I 0 1 1 b 0 0 1 c 1 1 0 l d 1 1 0 A 1 r 1 I 0 o 0 0 1 0 …