Questions asked by Luminous Grasshopper

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• Let S={v1=(2,2,3), v2=(-1,-2,1), v3=(0,1,0)}. Find a condition on a,b, and c so that v=(a,b,c) is a linear combination of v1,v2 and v3?
  
• If the matrix has free variables. Is it automatically linearly dependent?
  
• For the following set of vectors, determine whether it is linearly independent or linearly dependent. If it is linearly dependent, find all its maximum linearly independent subsets? {(1,2,-1),(2,4,6),(0,0,-8)}
  
• Permutation of lottery?
  
• Is the series converge or diverge?
  
• Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x)=0 for x<=0 and 0<F(x),1 for 0<x. Prove that if P(X>x+y|X>x)=P(X>y), then F(x)=1-#e^(-lamdax# , 0<x ?
  
• Let W1={A|A∈M2x2, A'=A} and W2={A|A∈M2X2,A'=-A} Prove that M2x2=W1+W2 (direct sum)?
  
• Let V=#RR^3# and W={(x,y,z)|x,y,z #in# #QQ#}. Is W#<=#V? Justify your answer.
  
• How do I evaluate this? #|(1+i)^50|#