For each part, determine whether the set of three functions is linearly dependent or linear independent on the interval (-0, 0). • If you say lin. dep., then display a dependence relation among f1, f2 and f3. That is, fir constants k1, k2, k3, not all zero, so that k1 f1(x) + k2 f2(x) + k3 f3(x) = 0 for all x. Or, equivalently, show that one of the three functions is equal to a linear combination of the other two functions. If you say lin. indep., you arc not requircd to prove that hcrc. (a) fi(x)= x, f2(x) - х+ 1, f3(x) = x + 2 (b) i() — е*, f2(x) = xe", f3(x) = x²e* (c) fi(x)= 0, f2(x) = e¬", f3(x) = e3r

For each part, determine whether the set of three functions is linearly dependent or linear independent on the interval (-0, 0). • If you say lin. dep., then display a dependence relation among f1, f2 and f3. That is, fir constants k1, k2, k3, not all zero, so that k1 f1(x) + k2 f2(x) + k3 f3(x) = 0 for all x. Or, equivalently, show that one of the three functions is equal to a linear combination of the other two functions. If you say lin. indep., you arc not requircd to prove that hcrc. (a) fi(x)= x, f2(x) - х+ 1, f3(x) = x + 2 (b) i() — е, f2(x) = xe", f3(x) = x²e (c) fi(x)= 0, f2(x) = e¬", f3(x) = e3r

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

For each part, determine whether the set of three functions is linearly dependent or linear
independent on the interval (-0, 0).
• If you say lin. dep., then display a dependence relation among f1, f2 and f3. That is, fir
constants k1, k2, k3, not all zero, so that k1 f1(x) + k2 f2(x) + k3 f3(x) = 0 for all x.
Or, equivalently, show that one of the three functions is equal to a linear combination of the other two functions.
If you say lin. indep., you arc not requircd to prove that hcrc.
(a) fi(x)= x,
f2(x)
- х+ 1,
f3(x) = x + 2
(b) i() — е*,
f2(x) = xe",
f3(x) = x²e*
(c) fi(x)= 0,
f2(x) = e¬",
f3(x) = e3r

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