Prove Linear Dependence for Set of Vectors w/ Zero Vector

eyehategod · Nov 4, 2007

I have to prove that any set of vectors containing the zero vector is linearly dependent.
How can I approach this?

sdobbers · Nov 4, 2007

(C1)(X1) + (C2)(X2) + ... + (Cn)(Xn) = 0

Take X1 = 0 vector; and all other constants besides C1 to be zero.

(C1)(0) + (0)(X2) + ... +(0)(Xn) = 0

In this case, C1 does not have to be equal to 0, it could be any number. In order for them to be independent, c1=c2=cn=0; since c1 does not equal 0 therefore they're dependent.

This is the way my professor described it to me, hopefully this helps.

eyehategod · Nov 4, 2007

thats it? thanks a lot bro, I get it now. \m/

Prove Linear Dependence for Set of Vectors w/ Zero Vector

Thread 'The colorful world of ##2\times 2## complex matrices'

Thread 'When are Markov Matrices also Martingales?'

Similar threads

Hot Threads

I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional

I How do we distinguish two different notations for cokernel and coimage?

I Localising a non integral domain at a prime

I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?

Recent Insights

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers