Linearly Definition and 217 Threads

Question: Prove that the list (x^3, sin(x), cos(x)) is linearly independent in V (V being the vector space of real-valued functions. In other words... common everyday math) They're linearly independent, its pretty obvious. The issue is -- proving rigorously. This is not for an assignment, its...

just a quick one: Homework Statement Show that the vectors a=2i -2j, b=3j - k and c = i + 2j +k are linearly independant Homework Equations The Attempt at a Solution What does 'linearly independent' mean and what's the test for it? Its from a really old exam paper so i might...

Three vectors are linearly independent iff The vectors are not on the same plane. Three vectors are linearly dependent ⇔ The vectors are on the same plane. Is this true.

I'm having trouble understanding what to do for this problem. The question I'm trying to answer is: Find 3 linearly independent solutions to the following differential equation, y^(3) + 3y'' + 3y' + y = 0. I really don't know how to even start this problem and what I'm really looking for. I...

A question on a General Relativity exam that I have asks how many linearly independent Killing fields there can be in an n-dimensional manifold. I'm sure I've seen this question before and I think that the answer is n(n+1)/2, but I can't remember why! Any help?

I don't know if this is a rule, but can a set of vectors be linearly independent if their determinant is not equal to zero? say 4 vectors are given in R^4, if I took the determinant of the 4 vectors such that det{v1 , v2, v3, v4} is not equal to zero, could i say that these vectors are...

Find a linearly independent set of vectors that spans the same subspace of R^3 as that spanned by the vectors \left(\begin{array}{c} -2 & -1 & -2 \end{array}\right) , \left(\begin{array}{c} -2 & 3 & -8 \end{array}\right) , \left(\begin{array}{c} 0 & -2 & 3 \end{array}\right)...

Show directly that the following functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the funtions that vanishes indetically. f(x)=17, g(x)= 2sin^2 x, h(x)= 3cos^2 x Do you just take the 1st and 2nd derivatives and do the determinate?? I am so...

You need to rotate the polarization direction of some linearly polarized light by an angle φ. That is, the light is initially linearly polarized along some direction (let's call it the y direction), and you need to change it so that the polarization direction is φ away from the y direction. In...

determine following setd of vectors in F(-infinitity, infinitiy) are linearly independent (using appropriate identities) 0, [cos (pi*x)]^3 , [sin 3*pi*x]^5 pls help !

f1(x)= (sqrtx) + 5, f2(x)= (sqrtx) + 5x f3(x)= x-1 i don't know how to start

[sin(t) , cos(t), e^t] are these linearly dependent? can someone solve this q? I write Asint+BcosT+C(e^t) = 0 but then i cannot proceed...

I just want to make sure I'm clear on the whole linearly dependent thing. If I find the Wronskian of a set of functions and it comes out: 12x^2 + 12x This would indicate that my set of functions is linearly dependent if the interval included x=0 and would be linearly independent if x...

I HAVE searched the threads before posting this but I didn't find the same question. Anyway, the question is T-F: A subset of linearly dependent set is linearly dependent. I think it is F, because for non-zero linearly dep. set a proof can be constructed so that some...

I have a couple of questions on this subject that I need help with. 1. Let v1, v2 and v3 be three linearly dependent vectors. Prove or disprove that the following vectors are also linearly dependent: v1+v2, v1+v3, v2+v3 2. Let S = {v1, v2, v3, v4, v5} be a set of five vectors in a vector...

I have a question from my assignment which requires me to prove that a sequence converges to 0 linearly, and another sequence that converges quadractically. I have no idea how to do this. The prof didn't talk much about it neither have the TA. The textbook book just gives the following about...

Hello. I want to ask questions... I hope you can guide me in showing the proof. 1. Let a, b and c be vectors in a vector space such that {a, b} is linearly independent. Show that if c does not belong to span {a, b} , then {a, b, c} is linearly independent. I know that is {a,b}...