test1

test1 - Math 107: Linear Algebra and Differential Equations...

This preview shows pages 1–7. 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: Math 107: Linear Algebra and Differential Equations Test #1 Name: I Thursday, October 1, 2009 ' All answers must be justiﬁed. Question 1. [10 points] (a) Find the inverse of the following matrix (b) Use the inverse to compute the solution to the system of equations 43—23; = 5 2:12—3y = )(zv-i we Question 2. [16 points] Suppose that A and B are two 71 X n matrices with det(A) = 3 and def; (B) = 7. Compute the following: (a) det(ABA) z 3x1}x57 63‘ (b) det(A—1) = 1/3 Question 3. [20 points] Consider the system of questions with unknowns 3'31, 352,” 3332 (13:1 + .713 = 1 — (1)332 + 2163 = 4 20ml + (b — a)32 + 323 = 2 (a) Determine the conditions on a and b so that the above system of equations admits a unique solution. a o [it a 0 I?! O 6 If! . i 0 2:1}(2’5 O L—dk [‘2 A 0 5‘“. (:2. 2a 5..“ I}? CKDDlD a a 0‘0 (b) Determine the conditions on a and b so that the above system of equations has @ solution. baa, Question 4. [10 points] Under what condition on the constants a and b is the vector [Z] in the linear span of the vectors: a * (I . "310‘ [2H Zzuh 245t0kee'0'glkaa ' ’9 o—{Ozlo-Jr 746m YME I ' (Zizi o—Bt 0L"2 '49 O o o: /?/Z(0\‘23 Question 5. [14 points] Given OH? 1%.? Wage 9 dfmﬁNSmD 52L Two [QR/of? —? db :2. Question 6. [15 points] (a) Show that the set satisfies the conditions for being a. subSpace of R3. (91+ (Mimi/IS ‘5) (x20, gab) C2) CCmecl W @0106?th Question 7. [20 points] (8.) Determine whether HE} [E]? [52]} form a spanning set for R3. Explain your answer. a l e—f IX 63f? 5: C g "7 Wot (“HQ/c3 “mad [c] i £31625 ’1' g g __H‘C O Q—ZZ‘C‘30K ﬂ . a t a“ —+ I Back 0 o 45ngc—3a’Q—2a)?‘ «jer {mad qbw‘ciéé (Levee/“(fan V 1am wgPammﬂ 56” 7%” W: (10) Does V above form a basis for R3? Why or why not. Yaglo (WWBVEICJFDFS ...
View Full Document

This note was uploaded on 04/25/2010 for the course MATH 107 taught by Professor Trangenstein during the Fall '07 term at Duke.

Page1 / 7

test1 - Math 107: Linear Algebra and Differential Equations...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online