Wronskian Suppose that f and g are differentiable functions on the unit interval I. The Wronskian of

Question:

Wronskian Suppose that f and g are differentiable functions on the unit interval I. The Wronskian of f and g is given by

Show that if W[f, g] (t) ( 0 for all t in I, then f and g are linearly independent. If c1 f(t) + c2g(t) ( 0, then c1 f' (t) + c2g'(t) ( 0; use Cramer's Rule to solve for c1 and c2?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

See More Books

Question Posted: May 26, 2016 06:03 AM

See More Questions

Suppose that f and g are differentiable at 2 and 3 with f'{2) = a, f'(3) = ft, g'(2) = c, and g'(3) = d. ft. If f(2) = 1, f(3) = 2, g(2) = 3, and g(3) = 4, evaluate each of the following derivatives....
Suppose that f and g are differentiable on an open interval I and that a R either belongs to I or is an endpoint of I. Suppose further that g and g' are never zero on I {a} and that is of the form...
Suppose that f and g are differentiable on [0, e] and that f' and g' are integrable on [0, e]. a) If e1 f(x)/xdx b) c) If 0 {f(0), g(0)} {f(e), g(e)} prove that f (a) log x dx 0. e* (f (x) + f,...
Identify possible opportunities for denormalizing these relations as part of the physical design of the database. Which ones would you be most likely to implement
Was Toscano entitled to reliance damages? Joseph Toscano was the general manager of Fields Pianos (Fields) in Santa Ana, California. He was unhappy with his job and decided to seek other employment....
You are building inspector in your local community. The emergency manager has asked you to create a report on building construction practices. What should you include in the report?
For each of the following situations, calculate the degrees of freedom $(d f)$, identify the critical values (assume $\mathrm{a}=.05$ [two-tailed]), calculate the $t$-statistic $(t)$, make a...
Indicate whether each of the following is true or false. If an answer is false, explain why. ______ 1. Insolvency means that a debtor has more current liabilities than current assets. ______ 2....
c) What is the output of the code fragment? public class Packagel { int type; double price; public static void main(String[] args) { Packagel pl = new Packagel (); } System.out.println(pl.type + " "...
Use the fact database and patron collection created in the text for use with MongoDB. Create a new document in the patron collection. The document should satisfy the following requirements: First...
A Questionable Basis: Is the set A basis for R3? If not, change one of the vectors to form a basis? 211 011 110
Zero Wronskian Does Not Imply Linear Dependence: We saw that a nonzero Wronskian implies linear independence but that the converse is not true. (see Example 12.) Another Example follows: (a) Show...
The following information concerns production in the Forging Department for June. The Forging Department uses the average cost method. a. Determine the cost per equivalent unit. b. Determine cost of...
A) Assuming that there are only 2 airline companies in the U.S. flying between Newark and Miami, Delta and Continental, what is the ((Nash) Equilibrium) or price that each company in the following...
Background AKA is a company working in the technology industry which, after having researched the market for gizmos, is now ready to launch a new product. Depending upon the success of this product,...
Annual interest rate is 5%. If you deposit 10,000 yen now, how much can you get after 1 year? The answer should be the total of principal and interest.
youd like to buy a 40 foot used catamaran in 10 years. you forecast that youll need $450,000 for the purchase at that time. how much should you save each month to reach your goal? the interest rate...
Go to BEA.gov and in the U.S. Economic Accounts find Table 1.1.5 (nominal GDP) and Table 1.1.6 (real GDP) and download them for the period 1960 to the latest available year in annual frequency...
In Exercises let Find a value of c for which the equation (x) = c has no solution. f(x) = 5-x, x3 -x + 6x8, x> 3.
CLASS PERIO Solving Linear Equations: Variable on Both Sides Solve each equation. 1) 6r+ 7 = 13 + 7r 3) -7x-3x+2=-8x-8 5)-14 +66+7-26=1+5b 7) n-3n = 14-4n 2) 13-4x=1-x 4)-8-x= x - 4x 6)n+2=-14-n 8)...
In Problems 18, determine whether or not the given vectors in R n form a basis for R n . v 1 = (0 , 7 , -3), v 2 = (0 , 5 , 4), v 3 = (0 , 5 , 10)
In Problems 18, determine whether or not the given vectors in R n form a basis for R n . v 1 = (0 , 0 , 1) , v 2 = ( 0, 1 , 2) , v 3 = (1 , 2 , 3)
In Problems 18, determine whether or not the given vectors in R n form a basis for R n . v 1 = (0 , 0 , 1) , v 2 = (7 , 4 , 11) , v 3 = (5 , 3 , 13)
The Morrit Corporation has $1,200,000 of debt outstanding, and it pays an interest rate of 8% annually. Morrit's annual sales are $6 million, its average tax rate is 25%, and its net profit margin on...
As an Investor, if I purchase a Corp Bond with a Coupon rate of 9%, and I am in the 30% tax bracket, effectively what rate will I be earning? Hint: If I purchased a Muni-Bond with an 8% Coupon rate,...
How can performance management systems be used to identify and nurture high-potential talent within the organization ?

Wronskian Suppose that f and g are differentiable functions on the unit interval I. The Wronskian of

Question:

fa) g(t) = f(t)g"(t)-f'(t)g(t).

Step by Step Answer:

Wronskian We assume that the Wronskian function Wf g t ft g t f t g t 0 For every t 0 1 To s...View the full answer

Differential Equations and Linear Algebra

Students also viewed these Linear Algebra questions