Linear Dependence with Zero Vector: A Simple Solution?

eyehategod
Messages
82
Reaction score
0
I have to prove that a set that has the zero vector is linearly dependent. Can anyone help me out?
 
Physics news on Phys.org
As usual a set {x1,x2...} is linearly dependent if you can find constants (not all zero) such that c1*x1+c2*x2+...=0. What happens if there is only one vector? Doesn't that make it easy?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Conflicting definitions of linear independence
Replies
30
Views
501
Linearly independent vs dependent functions
Replies
3
Views
1K
Introduction to Linear Algebra: Solving Real-World Problems
Replies
10
Views
2K
Determining value of r that makes the matrix linearly dependent
Replies
4
Views
2K
Isomorphisms preserve linear independence
Replies
2
Views
2K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
Replies
15
Views
2K
Null space of dual map of T = annihilator of range T
Replies
1
Views
2K
Linear Independence of a Set of Vectors
Replies
6
Views
2K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
1K
Intro to Linear Algebra - Nullspace of Rank 1 Matrix
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top