Question: 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

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 that the Wronskian is zero for the functions

(b) Show that the function f and g are not linearly dependent but independent on (-(,().

if 120, f(t) =12 and g(t)=t|11=

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b f and g are linearly independent ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4790).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

In general, the Wronskian of f1, fn in b(n - 1) is the Determinant and f1, . . . ,fn are linearly independent, provided W(x) is not identically zero. Repeat Exercises 10-14 using the Wronskian test....

Independence Checking, Use the Wronskian to check the subsets of C(R) in Problems 1-3 for linear independence? 1. {5, cos t, sin t} 2. {et, e-t, 1} 3. {2 + t, 2 - t, t2}

Linear independence and linear dependence are properties of sets. We can thus naturally ask how the properties of linear independence and dependence act with respect to the familiar elementary set...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Requirement: A two-page summary report on Board of Directors effectiveness based on the attached paper. Attributes and Structure of an Effective Board of Directors: A Theoretical Investigation...

Hi, This subject is financial accounting, here is a short essay type question, approximately 5 paragraphs. ''Drawing on private interest theory, what powers do you believe the Australian Accounting...

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

I would like someone to help me towrite-up with impression and thoughts with your own words. I do not want summarize but provide your impression and thoughts only for at least one page. Journal of...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

In sample problem 39-7 we showed that the radial probability density for the ground state of the hydrogen atom is a maximum when r = a, where a is the Bohr radius, show that the average value of r,...

What political and religious beliefs and institutions gave Hebrew civilization its unique character and account for its important legacy to Western civilization?

Which normal form ensures that there are no partial dependencies in a relational database? Group of answer choices Second Normal Form ( 2 NF ) Shelton Normal Form ( SNF ) Third Normal Form ( 3 NF )...

You are the benefits manager in a firm metaphorically described as part of the rust belt, in Syracuse, NY. The average age of your 600-person workforce is

In Problems 18, determine whether or not the given vectors in R n form a basis for R n . v 1 = (2 , 0 , 0 , 0) , v 2 = (0 , 3 , 0 , 0) , v 3 = (0 , 0 , 7, 6) , v 4 = (0 , 0 , 4 , 5)

In Problems 911, find a basis for the indicated subspace of R 3 . The plane with equation x - 2y + 5z = 0.

In Problems 1214, find a basis for the indicated subspace of R 4 . The set of all vectors of the form (a , b , c , d) for which a = b + c + d.

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight line over 6 years to a value...

#12 Refer to the accompanying table, which describes the number of 'adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups...

Arctic Enterprises, Inc. freezes water into ice. The standard and actual costs for direct labor for the manufacture of 2,000 tons of ice are: Standard costs Actual costs 405 hours at $19.80 400 hours...