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2006 MATH 1025 Class test 2

2006 MATH 1025 Class test 2 - York University Faculty of...

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Unformatted text preview: York University Faculty of Arts, Faculty of Science Math 1025 Class Test 2 NAME (print): SIGNATURE: STUDENT NUMBER: Instructions: 1. Time allowed: 50 minutes 2. There are 5 questions on 7 pages. 3. Answer all questions. 4. Your work must justify the answer you give. 5. No calculators or other aids permitted. Page 1 MATH 1025 Test 2 February 24, 2006 1. Let 0 2 2 6 1 1 2 1 A _ 2 1 2 —-1 1 1 1 2 (a) (6 points) Compute the determinant of A. fir/V V; [47: I 7’71 54$ III; 00"!) __ 22/6 0—2— 0 .._. "1-2’3 2 "' “"23 O~l I Q") ___Q\, Page 2 MATH 1025 February 24, 2006 (b) (6 points) Find the 1-3 entry of A71. » ’ fix/J —\_ _,_—.—— ,_,__._ , Test 2 22E: [(3 12.! I 2/ 2:" I [2’ 3)! la 00’ tZ—H flit 12/):1ln[/”“<>1 \fivcfl‘j‘” / mg I I 2— 3 "-\Ci"/ mmvd" L g/I... __ w—I LULxICA F5 U53 7% (6 £1” (Daft/km, UC/dm (4/) - » x ./ 5' 7. i ’ an ‘x T W! ’ C A KO \ f‘jVQCMd/L/ XUA O \W “$365de C/CQ/q W7C _ . ‘7 5 r Ff \U/Cnfix/j a {V0 /fl C Page 3 MATH 1025 Test 2 February 24, 2006 (C) (6 points) Use Cramer’s rule to find the value of c where 2b+20+6d= 0 a+b+2c+d= 1 2a+b+2c—d= 0 a+b+C+2d= 0 Note: Only find 0. You must use Cramer’s rule. N0 marks will be given if you use any other method. 0 209-, o 2.,é ‘ L. \IOJI --* 9L "" C 1:. ‘ 1,701 2 I l 2... 2c, 7:. fl 0"!” ~'..j" 1 I2— ”" M r t "\ '\ lb'C/Lqp(c}/\ s tit/6% - Page 4 MATH 1025 Test 2 February 24, 2006 c d 21) 2a 20 2d . . g h _ 3n—b 3m—a 30—0 3p—d 2. (6 p01nts) Gwen that k l — 2, find f e g h . F“ 0 p 2f — j 26— 2 29— k 2h— l ,. f“ ”‘4“ I! show complete work. j (K C'CL C UL [1+0 €wfl=f 2*” a“ 2.22.4 'k’fci 22' 3’1‘5 3M4 33—6. 310—4 2 3 3M3 3 2 n o I H. 7C :2 g ‘7’; F: j 4% .257 am: 2j—k awe —) —L——I<—2 Page 5 MATH 1025 Test 2 February 24, 2006 3. (4 points) Let A and B be 3X3 matrices with det(A) = 2 and det(B) = —3. Evaluate det((3AT)_1 B2 A). Show complete work. MATH 1025 4. (6 points) Let A = [ 2 0 0 12—1 13—2 Page 6 Test 2 February 24, 2006 . For which values of /\ does Ax = A3: have nontrivial solutions? V Page 7 MATH 1025 Test 2 February 24, 2006 5. (6 points) Write the determinant of the matrix _______”—-——v as the sum of its nonzero signed elementary products and compute its value. Show your work. On} MW nonacro W d€MtnTmr¢L¢\ is?“ {I ,'—~ fr? My ewwm m 5%; r—xJ Ca r-raffo Ari; “+2: [pal/m od—cz'fiOvt (r/ a 3 é it) fit? and w ++1 :5 I~Um7W-;’ /,______J 7% &@7L’€ rminmf 1162: VQ/UC ,7 é!) 5("2—)(7)[F)(~3)( 0(1) /( (”M ”.2 ———o’ZIO. MC“ got PRIQ (DU dd’A-m/ Nd (3W6 / . The end ...
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