Get started today!

Good to have you back!
If you've signed in to StudyBlue with Facebook in the past, please do that again.

- StudyBlue
- Iowa
- Iowa State University
- Mathematics
- Mathematics 267
- Willson
- worksheet12p2

Samuel Y.

Advertisement

Group: Worksheet 12 pt.2 (xx7.3-4) 1. Either solve the following systems of equations or show that there is no solution. (a) 2x1 x2 + 3x3 = 1 x1 + x3 = 2 x1 + x2 + 2x3 = 1 (b) x1 + 2x2 + 2x3 = 2 x1 + 2x2 = 1 x1 + x3 = 1 2. Find the eigenvalues and eigenvectors for the following matrices. (a) (#18 pg 384) 1 i i 1 ! (b) (#18 pg 384) 0 BB @ 3 2 2 1 4 1 2 4 1 1 CC A 3. (#6 pg 389) Consider the vectors x(1)(t) = t 1 ! and x(2)(t) = t2 2t ! (a) Compute the Wronskian of x(1) and x(2). (b) In what intervals are x(1) and x(2) linearly independent? (c) What conclusion can be drawn about the coe cients in the system of homo- geneous di erential equations satis ed by x(1) and x(2)? (Hint: See Theorem 7.1.2 pg 359.) (d) Find the system of di erential equations and verify the conclusions of part (c). 4. (#4 pg 389) If x1 = y and x2 = y0, then the second order equations y00 + p(t)y0 + q(t)y = 0 corresponds to the system x01 = x2 x02 = q(t)x1 p(t)x2: Show that if x(1) and x(2) are a fundamental set of solutions of this system, and if y(1) and y(2) are a fundamental set of solutions of the second order equation, then W[y(1);y(2)] = cW[x(1);x(2)], where c is a nonzero constant. Hint: y(1)(t) and y(2)(t) must be linear combinations of x11(t) and x12(t).

Advertisement

"StudyBlue is great for studying. I love the study guides, flashcards and quizzes. So extremely helpful for all of my classes!"

Alice , Arizona State University"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim , University of Florida"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly! I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer , Rutgers University"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin , LSU
StudyBlue is not sponsored or endorsed by any college, university, or instructor.

© 2015 StudyBlue Inc. All rights reserved.

© 2015 StudyBlue Inc. All rights reserved.