Explanation Given: The statement is given below. If y 1 an y 2 are linearly dependent on the interval [ a , b ] , then y 1 and y 2 are linearly dependent on the smaller interval [ c , d ] ⊂ [ a , b ] . Approach: • Let y 1 and y 2 be two differentiable functions defined on some interval I and Wronskian (the determinant of these two functions such that W [ y 1 , y 2 ] ( t ) = | y 1 ( t ) y 2 ( t ) y 1 ′ ( t ) y 2 ′ ( t ) | ) is zero then the functions y 1 and y 2 are linearly dependent. If the Wronskian of these two functions is not equal to zero then the functions are linearly independent. Calculation: Consider the functions y 1 ( t ) = t e t and y 2 ( t ) = t 2 e t defined in the interval [ − 1 , 2 ] . And the Wronskian of these functions is given below. To determine ( b ) Whether the given statement is true or false.

7th Edition

ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

See similar textbooks

Videos

Question

Chapter 4.7, Problem 25E

To determine

(a)

Whether the given statement is true or false.

To determine

(b)

Whether the given statement is true or false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.7, Problem 24E

Chapter 4.7, Problem 26E

Students have asked these similar questions

Problem 1 An airport is served with an average of 10 departures per day to your desired destination. However, all these flights leave at random times. You are trying to decide how long you are willing to wait to catch the next flight after you arrive at airport. Part A: Acceptable waiting time: T [min] = 78min Part B: What is the probability there will be exactly one departure during this waiting time? Part C: What is the probability there will be exactly no departure during this waiting time? Part D: Which calculation (B or C) should you use to make your decision to wait or leave? Why?

Problem 5 Consider the hospital admissions table presented in the lecture: 刊 Outcome LWBS Admitted Hospital 1 195 Hospital 2 270 Hospital 3 246 Hospital 4 242 1277 1558 1350 984 Not Admitted 3820 5163 4728 3103 Part A: What is the conditional probability that you were admitted if you went to hospital 3? Part B: What is the conditional probability that you went to hospital 3 if you were admitted?

QUAT6221wA1 Accessibility Mode Immersiv Q.1.2 Match the definition in column X with the correct term in column Y. Two marks will be awarded for each correct answer. (20) COLUMN X Q.1.2.1 COLUMN Y Condenses sample data into a few summary A. Statistics measures Q.1.2.2 The collection of all possible observations that exist for the random variable under study. B. Descriptive statistics Q.1.2.3 Describes a characteristic of a sample. C. Ordinal-scaled data Q.1.2.4 The actual values or outcomes are recorded on a random variable. D. Inferential statistics 0.1.2.5 Categorical data, where the categories have an implied ranking. E. Data Q.1.2.6 A set of mathematically based tools & techniques that transform raw data into F. Statistical modelling information to support effective decision- making. 45 Q Search 28 # 00 8 LO 1 f F10 Prise 11+

Chapter 4 Solutions

EBK FUND.OF DIFF.EQUATIONS+BOUNDARY...

Ch. 4.1 - Verify that for b=0 and Fext(t)=0, equation (3)...Ch. 4.1 - If Fext(t)=0, equation (3) becomes my+by+ky=0. For...Ch. 4.1 - Show that if Fext(t)=0, m=1, k=9, and b=6, then...Ch. 4.1 - Prob. 4E Ch. 4.1 - Verify that the exponentially damped sinusoid...Ch. 4.1 - An external force F(t)=2cos2t is applied to a...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - Undamped oscillators that are driven at resonance...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.