MATH 218 Exam 1 with Solution, Fall 2009

AMERICAN UNIVERSITY OF BEIRUT Math2i8 - Fall 09-10 Instructor: N. Makhoul-Karam - Section 4 Brief Quiz t, - October 29 Na Me tesccmemmmmnnmaeae AUB ED number; ...........0.........005 Grade: 16 Question 1: {3 points) 123 1 Let A be the 3x3 matrix: A = (2 5 3) and b = (2) 1 4 8 0 Show that A is invertible and find A. Deduce the solution of the linear system AX = b. % Geet +he. reduced mew --echke ton Lor Tack “parferm than Deore. prow erpctaoto us on age rele Sercnal Ls to 2. B]i .8. a Rh SS 3/0 ta 1 6 B@fe. ao | Voz 3]\ .@ o R-2R, RB, . ( o lt 2 |. 1.0 R,-8,.. 8, Ont Slat ot fo. R 2 sa l o. 4% }48. 2 4 : Raat R, Ry ru] J -S3[-2. Ut Qa oes ® oa. cA fiS. 2 if glog FAK oe | se ; oO. L.-3li2 1 6 ~R, ky ( © oN ES. ce us .. BR GRs. KR, 4 o. oal40 16.9 R,+3R, =>, ( o s. of 1B 2G Ls. se fi] 6 Ch. Sw 2D onl The RREF of A oO fAkae | oe Lith, a) « es ab . (3) = % &\ ve) ce eee ang 8 qEDD) a8 2 & X={ 8] i ee Sis dls vl S$ 44 . 4 ? Lntgne : Selybos 4 AX=6 Question 2: (2 points) Find conditions that the b’s must satisfy for the following system to be consistent: % ty + = : =X, = 6, 5x, +43 + 3x, ~ 5, Bugrenies Nana bry, sumer alge te the "epee wi ft ot 1 b . , si (‘. wl o | a tt sho m Tow. echelon form aS 1. 3 Jb ss WY ‘ fl ‘ t by. TTT RR, aR ( (on ae “tots . BSR, —y TH... Oo ~¢ -2. } -Sheb, /..... a a 1 t on R,-27 aR, . CS a oe Se °o a. +) 3b, - ahebs “By yby and by Should sabiePy : ~Sb-2bth, 0. 2S. b= 3b 426, Question 3: (i point) Show that if A is invertible and symmetric, then A” is symmetric. A el, vy ry na Ads S Stenme be ( A= at) “Fede : KY as seqomabte :