Prove that the set of functions {eq}f_1(x) = x,\ f_2(x) = \cos 5x {/eq} and {eq}f_3(x) = \sin 5x {/eq} on the interval {eq}(-\infty,\ \infty) {/eq} is linearly independent. Linear Dependent And Linear Independen...
(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. ...
Consider the functions {eq}f(x) = e^x + e^{2x}, g(x) = e^x + 2e^{2x}{/eq}, and {eq}h(x) = e^x + 3e^{2x}{/eq}. Are these three functions linearly dependent or independent? The Wronskian and Linear Depend...
Forum: Linear and Abstract Algebra MHB 12.6 linearly dependent or linearly independent? Are the vectors $$v_1=x^2+1 ,\quad v_2=x+2 ,\quad v_3=x^2+2x$$ linearly dependent or linearly independent? if $$c_1(x^2+1)+c_2(x+2)+c_3(x^2+2x)=0$$ is the system $$\begin{arr...
ait is not difficult to verify that these two functions are linearly independent 核实是不难的这二个作用线性地是独立[translate]
If a nontrivial solution can be found, then we say that the set of vectors is linearly dependent. If only the trivial solution is satisfied, the set of vectors is said to be linearly independent. To illustrate the case of nontrivial satisfaction of the above equation, let us assume three...
The Wronskian of two functions is found to be zero at x0−ε≤x≤x0+ε for arbitrarily small ε>0. Show that this Wronskian vanishes for all x and that the functions are linearly dependent. 7.6.6 The three functions sin x, ex, and e−x are linearly independent. No one function ...
linearly independent[数]线性无关的;线性独立的 linearly dependent线性相关;线性相依 linearly词源英文解释 The first known use of linear was circa 1656 linearly儿童词典英英释义 linesmannoun an official who assists a referee in a game (as football or hockey) ...
The solution of the Schrdinger equation HK Ψ = E Ψ is discussed in terms of a basis Φ of n functions of which only p are linearly independent. After introducing a variable ∞ and the matrix K = Φ| H - ∞∞ 1|Φ} = H - ∞δ, a super-secular-equation |K - Δ. 1| = 0...
Linearly dependent subspaces and the eigenvalue spectrum of the one-particle reduced density matrix The structure of the one-particle reduced density matrix when expressed in a Cartesian Gaussian basis set is investigated. A set of exact linear dependency... GTSL Schmider - 《Journal of Molecular ...