2005 Math 1025 class test 1

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

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online