An arbitrary function defined in the function space thus constructed can be represented by a linear combination of the linearly independent functions and applying the inverse transformation to the solutions thus obtained, the authors can obtain the solution for the original equation of motion.doi:10.1002/eej.4390990116Hitoshi TakataJohn...
Let S = { f1(t), f2(t)} be a set of two functions. The set S is linearly dependent on an interval I if there are constants c1 and c2 not both zero, so that c1f1(t)+c2f2(t)=0 for every value of t in the interval I. The set S is linearly independent if S is not ...
FunctionsIndependentLinear independenceLinearly Replies: 21 Forum:Calculus and Beyond Homework Help IProving functions are linearly dependent We can make the first three functions add up to zero in the following way : ##\sin^2 t+\cos^2 t-\frac{1}{3}\times 3 = \varphi_1(t) + \varphi_...
(redirected fromLinearly dependent) Encyclopedia Related to Linearly dependent:Linearly independent linear independence n. The property of a set of vectors of having no linear combinations equal to zero unless all of the coefficients are equal to zero. ...
If υ is a nonzero vector then the singleton {υ} is a linearly independent set. d. If b and c are distinct scalars and υ is any vector, then any set containing both bυ and cυ is linearly dependent. e. A set S is linearly dependent if and only if some point s∈ S is in...
Determine whether the set of vectors {v - u, w - v, u - w} is linearly independent or dependent. Let u and v be any vectors in R^n. Prove that the span of {u,v} equals the span of{u+v,u-v}. Prove that ...
What do we mean when we say that two functions y1(x) and y2(x) are linearly dependent?Question:What do we mean when we say that two functions y1(x) and y2(x) are linearly dependent? Linear Independence:We can determine whether or not two vectors or two fun...
Suppose two functions f and g aredifferentiableon someintervalI. If W(f, g) (x) = 0 for all x in the interval I, the two functions are linearly dependent on I. If W(f, g) (x) &≠ 0 for some x0in the interval I, then the two functions are linearly independent. ...
The central limit theorem for stationary linearly dependent se- quences is extended for elements in the space of continuous functions on a compact metric space. The proof is based on a new estimate for exponen- tial-type moments of stuns of independent random variables. 1. Introduction Let x=...
linearly dependent b. linearly independent c. either a or b d. none of these View Solution If a, b, c are linearly independent vectors and delta =|(a,b,c),(a.a,a.b,a.c),(a.c,b.c,c.c)| then (a)delta = 0 (b) delta = 1 (C) A=any non-zero volue (d)None of ...