Give an interval over which the set of two functions f 1 (x) = x 2 and
Question:
Give an interval over which the set of two functions f1(x) = x2 and f2(x) = x |x| is linearly independent. Then give an interval over which the set consisting of f1 and f2 is linearly dependent.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 37% (8 reviews)
The given functions are f 1 x x 2 and f 2 x xx So f 2 x x 2 whenever x 0 x 2 whenever x0 ...View the full answer
Answered By
Goutam Biswas
I have completed post-graduation from the Indian Institute of Technology Gandhinagar in Mathematics in 2020. During my master's degree course, I was assigned a mentor in a mathematics course offered towards first year B. Tech students. That was a golden opportunity for me to teach and co-learn college-level math in a premier institute like IIT Gandhinagar. Also, I have participated actively in many tutorial sessions of courses for the fulfillment of my degree.
Algebra is one of the oldest branches of Mathematics which was primarily introduced to solve fascinating polynomial equations of several variables arising from various branches of physical sciences. But currently, the language of modern algebra has changed a lot keeping the core ideas and questions the same.
Writing rigorous proofs and solving problems in algebra were much different skills that I built up with the books of Gallian and Dummit and Foote. I studied the theory of Fields from Hungerford’s book and a few introductory chapters of Commutative algebra from the books of Atiyah Macdonald and Balwant Singh. I solved problems from the competitive test papers of renowned Indian institutes. I also encourage my colleagues and junior students to solve such problems and to show them to me if they get stuck.
0.00
0 Reviews
10+ Question Solved
Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
Question Posted:
Students also viewed these Mathematics questions
-
Consider the differential equation dy/dx = e -x . (a) Explain why a solution of the DE must be an increasing function on any interval of the x- axis. (b) What are What does this suggest about a...
-
Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and (f) the...
-
Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and ( f ) the...
-
It is reported that 85% of Asian, 78% of white, 70% of Hispanic, and 38% of black children have two parents at home. Suppose there are 500 students in a representative school, of which 280 are white,...
-
Use the table above to answer the following questions. a. What was the difference between the 52-week high and the 52-week low for one share of AT&T? b. What was the difference between the day's high...
-
Consider a cylinder with a length of 15 cm and a diameter of 10 cm. The cylinder has a surface temperature of 43C, while the room air temperature is 17C. Determine whether placing the cylinder...
-
Bickley Academy is a competitive private college preparatory high school. Bickleys administration is now considering applications from the three local junior high schools: Montgomery, Cleeghorn, and...
-
Landen Corporation uses a job-order costing system. At the beginning of the year, the company made the following estimates: Direct labor-hours required to support estimated production . . . . . . . ....
-
What is the difference between tacit and explicit knowledge? describe an example of each. How might an organization manage tacit knowledge?
-
On January 1, 2019, Triple A Company acquired Bodyguard Companys outstanding common stock for $842,000 in cash. As of that date the following information was acquired from Bodyguard, the subsidiary...
-
If y 1 = e x and y 2 = e -x are solutions of homogeneous linear differential equation, then necessarily y = -5e -x + 10e x is also a solution of the DE. _____ Answer problem without referring back to...
-
Without the aid of the Wronskian, determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval. (a) f 1 (x) = ln x, f 2 (x) = ln x 2 , (0, )...
-
How well is data shared in the building process?
-
When evaluating platforms, what is the key factor in ensuring a platform addresses an organizations needs?
-
Smart Coffee is an internationally operating company that sells premium coffee to restaurants, delicatessen stores, and wholesalers. They want to develop a new distribution concept for the DACH...
-
Create a macro function to estimate the Macaulay duration. calculate Macaulay duration is by using the following formula: D 1 + r + [Nx (c r)]) cx [(1+r)N 1] + r) 1+" _1 }-(-/-) where c is the...
-
Tom did not want his POLS&200 textbook anymore after the quarter ended, so he threw it in the garbage can in Mary's Caf. Bob saw it there and took it, as he was planning on taking POLS&200 next...
-
When the breach was discovered and the logs were reviewed, it was discovered that the attacker had purged the logs on the system that they compromised. How can this be prevented in the future?
-
List three categories of receivables. State how each category is classified for reporting on the balance sheet.
-
Rewrite the code of Figure 7.3 in Ada, Java, or C#. Figure 7.3: template class queue { item items [max_items]; int next_free, next_full, num_items; public: queue () : next_free (0), next_full(0),...
-
What is Web Analytics? Discuss the application of Web analytics for businesses.
-
Define SEO? What does it involve? Discuss the most commonly used methods for SEO.
-
What is PageRank algorithm? What is the relation between PageRank and citation analysis? How does Google use PageRank?
-
3. Show that : -3t = y 3 sin(t) cos(t) + e is a solution to the differential equation y' + 3 y 10 sin(t)
-
The United States, Austrailia, Canada, and the United Kingdom cluster high on individualism but low on power distance on Hofstede\'s cutlutral graph. What does this mean to someone looking to market...
-
Mini-garden project Week one of the mini-garden project involved Sacha and her fellow pre-schoolers planting sunflower seeds into the outdoor garden bed. Each child in the activity has been assigned...
Study smarter with the SolutionInn App