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midterm1 2008 - 5w10617 4.LetA= 2 —4 313 3 m6 3 0 3 1 m2...

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Unformatted text preview: 5w10617 4.LetA= 2 —4 313 3 m6 3 0 3 1 m2 0 “I 0 1 —-2 D —-1 0 B: O O 5 5 0 andC': O 0 1 0 0 1 __2 D “I 1 0 0 0 0 1 (20 pts.) a) Find an invertible matrix P such that PA = B . \ .. ’2__ 0 «l a v1. i I} _+ #2. o o t l O ”T e C) 5‘ O l , ' it «’2, 0 ~( 0 (Bill ”2 “*7 o o t \ 0 GP ,, w.» ' 3: \Ce‘ tier—B Pu. ~23“ ‘0 A W P 1 «~32, O M. iwLe>~’\O AQ‘JLO 0 o\fi?\rx L \ C) 3 C) ’0 t ‘l i ”'1. o _,._ ‘ O c '52 Le 6 L a C) 2 R Q 0 0 t5 0 1 R A .1, K (3 mm. (‘ow rd. flcinelcn A 33? RR R 32 ‘L a... out; .3 c} ‘93 Jdi‘vg ’Ekwéw'd A ) are UJ 411mb fiifti a f\ ‘L Hive“ ‘3 '7‘ A94)" L Ué’ WM; (:32 jgcwk Mmkf‘rcci- S. {alga-L Ril “ C are” fia‘i’ M E T U c Department of Mathematics Basic Linear Aigebra Midterm I Code : Math 260 Last Name : Acad. Year! 2008 ‘ . Semester :Feu Name - Student No- Department: Instructor 1 Signature . Date 3 26.03.2008 , Time . : 17.40 4 Questions on 4 Pages Duration I .90 minutes Totai 100 Pomts I'll-ll-H Show your work! Partial credits will not be given for correct answers if they are not justified. 1.Let 1 Z—k 1 3+.Ie ‘ m, ‘1 2m 1 6+2}; 1“ "” 2 4~2k 3 6+2k; —1_ 0 m1 ~3—k (15 pts.) a) Find the values of k- for which the matrix A is invertible. \. a :9 c) A ,r nee—a -w) o 14:— o 0 e9 ‘3 l O 0 o o eile (20 pts.) 2. 3) Find the general soiution of the foilowing system. —2221 -— 2mg — 10x3 + 934 + 235 m "“15 3531 + 3562 +1533 — 934 n 2:65 = 21 331+3$3m375=4 a b ”3. <5 *3— l l (5 i \ 14.,” 0 (j d O \ 2., M . . ”Lo/L. Amy“? we}: fix. HM $33W . ~3 ‘59. :- «l. ‘41, \ + Xg t O 1’ X3) (3 1‘5 ,5 (3 m 0 (10 pts.) b) Find a solution of the above sytem which satisfies :34 = 1 and 233 = 0. U (10 pts.) 3. Find the determinant of the matrix 16 15 14 13 Am 121110 9 and 8 7 5 5 4 3 2 1 decide the invertibility of A. a. 1 Qz’t Q1 Li, at LL 5' A _,........p w ‘L U 5: Cl ‘1 L(' P K +8 1 ‘* 3 a 3 .L 1 Qmi an; tL—éln 11‘0”” ‘9”; M (die/JCCAJ‘7O (55> Ate/+18]: O a” ‘L g Mi oLeArLN 22—0 A 9‘} R’uef £*L(fii , ...
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