06jesher44395
04.07.2020 •
Mathematics
Are the functions f,g, and h given below linearly independent?
f(x)=e^4x
g(x)=xe^4x
h(x)=x2e^4x.
If they are independent, write all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.
A(e^4x−cos5x)+B(e^4x+cos5x)+C(cos5x)=0
Solved
Show answers
More tips
- S Sport How to Learn Swimming? Simple Tips for Beginners...
- P Photography and Videography Understanding HDR: How It Works and Why You Need It...
- G Goods and services Which TV is better - LCD or Plasma?...
- S Sport How to Learn to Pull Up on Monkey Bars?...
- L Leisure and Entertainment Scrapbooking: What is it and Why is it Becoming More Popular?...
- C Computers and Internet Where did torrents.ru move to?...
- B Business and Finance Understanding Cash Flow: What It Is and How It Works...
- C Computers and Internet What Are Peers and Seeds in Torrenting?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
Answers on questions: Mathematics
- M Mathematics What is the volume of this cylinder tank (in cubic feet, to three decimals)? (Remember for cylinders V=pi x radius squared x h)...
- M Mathematics Determine the present value p you must invest to have the future value a at simple interest rate r after time t. a = $18 comma 000, r = 4.0%, t = 2 years...
- M Mathematics Ginnifer runs 2mph faster than Sumalee. They run in opposite directions for 1.5 hours. They are now 15 miles apart. How fast does each girl run? A. Sumalee = 5; Ginnifer 5 B....
- M Mathematics The equation of the line shown in the graph is y = ?....
- W World Languages Are the french and italian languages the same?...
- M Mathematics What is the solution to the linear equation? d - 10 - 2d + 7 = 8+ d - 10 - 3d...
Ответ:
Linearly independent, x = 0
Step-by-step explanation:
- We are given three functions as follows:
- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:
Where,
c1 , c2 , c3 are all zeroes then for all values of (x),
- The system of function is said to be linearly independent
- We will express are system of equations as such:
- To express our system of linear equations we will choose three arbitrary values of ( x ). We will choose, x = 0. then we have:
- Next choose x = 1:
- Next choose x = 2:
- Solve the last two equations simultaneously we have:
.... ( Only trivial solution exist )
The functions are linearly independent
- The only zero exist is x = 0.
Ответ: