1. S

    Linear (in)dependence

    Hi guys, I'm stuck with a problem which is, I believe, simple, but I can't solve it by myself. So, I have 4 vectors a,b,c,d that are linearly independent. I am supposed to check whether the following vectors are dependent or independent: a1 = a+2c+d b1 = 2a-b+c c1 = a+c+d Thank you in advance. :D
  2. S

    Linear independence of functions

    Whether Cos 3x and Cos (3x + Pi/2)are linearly independent or not in the interval (-infinity, infinity)? My attempt: I calculated the Wronskian that comes out to be -3 (independent of x) that signifies that this function is linearly independent because the sufficient condition for the set...
  3. P

    Feedback for an answer involving Span, Dimension and Linear Independence

    Hi guys, I have worked out an answer to the following question, but it's stretching my understanding of Linear Algebra to the limit, so… if anybody could have a look at it, and just tell me whether my reasoning is sound, it would be a great help... Let v_1,…,v_k,u,w be vectors in the...
  4. Z

    Probability and Independence

    Let A, B, C, D, E be five boolean random variables. Assume that you are give the independence assumptions: * A and B are independent absolutely. * D is conditionally independent of both A and C, given B. * E is conditionally independent of A, B and D, given C. Assume you also are give...
  5. Z

    Linear Independence Question #2

    Am I correct that if a matrix A_{m ~X~ n} (m < n) and its rank is m. Since it has some free variables. By definition the matrix A is linear dependence. Please review the following matrix A 1.000 -1.000 1.000 5.000 -2.000 3.000 1.000 2.000 3.000 4.000 -2.000 3.000 My...
  6. B

    Linear dependency and independence

    Can this be explained by use of one solution, no solution or infinitely many solutions? If not, just summarize it for me the way you understand it. Sent from my SM-G955W using Tapatalk
  7. M

    Linear independence

    For what real values of x do the vectors v1 = (1, 2, x), v2 = (1, 1, 1) and v3 = (x, 6, 2) form a linearly dependent set?
  8. W

    By The Independence......

    The following is part of a solution to an example problem. I am starting in the middle since I have a question about a step in this solution...... (1) E\big [\sum^N_1 X_i \big]=E\big[ E\big [\sum^N_1 X_i \big| N \big] \big] BUT (2) E\big[ \sum^N_1 X_i \big| N=n \big] =E\big[\sum^n_1...
  9. C

    Independence in probability

    I made plenty of exercises with independence in probability but this question seems quite strange; are events always independent of themselves? Obviously not--that would be the case only if P(A) was equal 0 or 1. But now I'm a little bit confused about what do we understand by (A n A) in...
  10. A

    p(a,b,c)=f(a,c)g(b,c) implies independence

    A, B and C are three discrete random variables. I need to prove that the following two statements are equivalent: a) A and B are independent given C b) p(a,b,c) = f(a,c) * g(b,c) for some functions f,g I can easily show that a) implies b), but I don't know how to show that b) implies a)...
  11. L

    Linear Independence and Linear Dependence.

    Find n.m vectors LI in $M_{nXm}\left ( \mathbb{R} \right )$.
  12. L

    Linear Independence and Linear Dependence.

    On each item to determine whether the vectors of the vector space V are LI or LD. b) $x-1,x^{2}+1$ and $x^{3}-x^{2}-x+3$ in $V=P_{3}(\mathbb{R})$
  13. L

    Linear Independence and Linear Dependence.

    If $\left \{ u,v \right \}$, $\left \{ v,w \right \}$ and $\left \{ w,u \right \}$ LI are subsets of a vector space V, then $\left \{ u,v,w \right \}$ is LI? Note: LI is Linear Independence.
  14. L

    Linear Independence and Linear Dependence.

    Prove that the three vectors are $\mathbb{R}^{2}$ LD (Linear Dependence). Generalize this result to $\mathbb{R}^{n}$.
  15. A

    Linear independence & linear dependence

    Suppose that vectors v1,v2,v3 are linearly independent. (i) Prove that v1-v2, v2-v3 and v3-v1 are linearly dependent. (ii) Prove that v1+v2, v2+v3 and v3+v1 are linearly dependent. I need you guys to help me solve this question because I'm stucked in this question for few hours already :(...
  16. M

    Linear Independence

    Are the matrices 1 1 1 1 0 -1 1 0 2 0 0 2 0 1 -1 -1 linearly independent? Can you show me how you obtain the answer?
  17. X

    Help for Linearly Independence

    Let A and B be two matrices such that C = AB exists (i.e. the matrices can be multiplied). If the columns of A and the columns of B are linearly independent does it mean that the columns of C are also linearly independent?
  18. C

    Proof by contradiction of linear independence

    SOLUTION: proofs kill me! S=(v1,v2, is a linearly independent set of vectors in the vector space V, prove that any nonempty subset of S must be linearly independent. I know that a This is a link I stumbled upon on my travels- I understand it all, apart from the line where 0B_f+0B_g etc is...
  19. H

    Linear independence proof?

    I've been given the following assignment: Assume that the vectors w1=u+iv and w2=u-iv are linearly independent. Then, the vectors u and v are also linearly independent. Provide a proof of this. I've been starring into the paper for half a day now and the answer still eludes me. Any...
  20. B

    Prove for Linear Independence

    If W = {v1,v2,v3,v4} are orthogonal, {vm,vn}=0 for m does not equal n, then they are linearly independent please help! thanks!