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.
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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
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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.
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Related Book For 
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
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