2005 Math 1025 class test 1

2005 Math 1025 class test 1 - York University Faculty of...

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Unformatted text preview: York University Faculty of Arts, Faculty of Science Math 1025 Class -: 1 _ . .r , NAME (print): A\_r (Family) / \ (Given) SIGNATURE: STUDENT NUMBER: A I ‘ Instructions: [L— Questior_1_‘ Points LMarks 1. Time allowed: 50 minutes 1 11 2. There are 5 questions on 5 pages. 3 g 3. Answer all questions. 4 7 l: . . . 5 7 4. Your work must Justlfy the answer you glve. Total 40 5. No calculators or other aids permitted. Page 1 MATH 1025 Test 1 January 27, 2005 1. (11 points) (a) Solve $1 —2:r2 +4334 2 3 21121 —41122 +1123 +6224 = 7 41m ~8x2 +rr3 +14x4 = 13 —.2 0 L743 O/(j I/Ll X, —3+01§"L/'~C‘ C) a / VZ‘ l. XL: . 33—526 ’/~«20 it“s V3,; 0 O l“@( xi“ 0 o 0 @(® (b) Are there solutions to the system in (a) which satisfy the additional equation x1 —2x2+:r3+2x4=5 ? Give one or explain why none exist. (3tu+%£)*25+(l+2t)+3t7f:5 ' 7:5 )MFOSEIL/Q No 6‘0 lJf’To M‘ (0) Are there solutions to the system in (a) which satisfy the additional equation $1—$2+$3+$4=5? Give one or explain why none exist. Page 2 MATH 1025 Test 1 January 27, 2005 2. (7 points) For which values of I: does the system 3: +21 +2 2 2 23: +3y +22 = 3 23: +33; +(k2—2)z = k+5 have (a) no solutions? (b) aunique solution? (c) an infinite number of solutions? Your work must justify the answer you give. ' f / J 2 2 3 Z 3 Z 3 k2,"; [CH I I / g; o I 53 __ o f (<24 W l l l a <7 I 0 fi’ 0 c) b‘l KJF (a f< : a / mt row 0 7L i QJ7L VOV 7? O [(2. (b) \ \% a Fé‘duceg +0 7- Page 3 MATH 1025 Test 1 January 27, 2005 3. (8 points) Let (b) Determine A—1 . _{ [ad 74 3 0/0 GO" 00! 0/930 : L/O‘“3 €01 040 Page 4 January 27, 2005 Test 1 MATH 1025 4. (7 points) Find A‘l, where Page 5 MATH 1025 Test 1 January 27, 2005 5. (7 points) Let A be the 2 x 2 matrix, A = [ (Z 3 ] . Recall that tr(A) = a+d and det(A) = ad— bc. (a) Show that A satisfies the matrix equation A2—tr(A)A+det(A)I=0. fl2*(&+c()/} + [act—’59: / O /::{)w[a+c€)(jj)‘7/M’écjéfl /) :(fiwc at+M)_ $427?ch “Ma/2t (b) Let A = [ 12)) i ] . Find numbers k,l such that A2 + kA + H = 0. kS’éff/t) 3“"3 fl rat/€04): - / The end ...
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2005 Math 1025 class test 1 - York University Faculty of...

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