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#math
<tjcoder_> there's no case where you have >= 2 aces but not >= 1 ace
<asphyxia> the probability of having to aces given you know you already have one should be much greater than not knowing you have one
<tjcoder_> well yeah
<tjcoder_> P(>=2 aces | >= 1 ace) = P(>= 2 aces ^ >= 1 ace) / P(>= 1 ace)
<asphyxia> true
<tjcoder_> but since you know you have >=1 ace if you have >= 2 aces, it's just P(>= 2 aces) / P(>= 1 ace)
<asphyxia> you dont know, thats the point
<tjcoder_> what don't i know?
<asphyxia> oh, I give up
<asphyxia> I have to do my own assignment :|
<tjcoder_> sorry if i'm slow :-S but thanks for your help.
<asphyxia> dont worry, Im the slow part
<_shellcode_> How would I find a spanning set for nullspace(A) where A is the 3x3 matrix {(1,2,3),(3,4,5),(5,6,7)}?
<Mulder> use the nop luke!
<Mulder> i think you just solve for Ax=0, and then row reduce?
<_shellcode_> I set Ax=0 and find x=<t,-2t,t> but I don't really understand from that point...
<_shellcode_> Right, thats the nullspace
<_shellcode_> but what is the spanning set?
<me22> (1,-2,1) ?
<Mulder> once you row reduce to echelon form, the spanning set becomes trivial
<_shellcode_> But how can a vector have a spanning set?
<Mulder> or even, reduced echelon form
<_shellcode_> Doesn't something need to be a vector space to have a spanning set?
<gzl> _shellcode_: the null space is a vector space.
<asphyxia> _shellcode_: If you row-echelon reduce the matrix A, the nullspace will be clear...
<_shellcode_> Ok. I think I get it.
<asphyxia> the dimension of the nullspace is given by the rank.
<gzl> no it isn't.
<asphyxia> as you have that the rank (dimension of rowspace) + dimension of nullspace (nullity) gives you 3
<_shellcode_> er...huh?
<asphyxia> or n, for a random matrix with n rows.
<asphyxia> gzl: is that untrue?
<gzl> that is true, but it's misleading to say that the rank gives the dimension of the nullspace. it sounds like you're telling him rank = nullity
<asphyxia> oh, yeah
<asphyxia> I know I was inspecific.
<asphyxia> _shellcode_: But, point being, the number of rows consisting of only zeros are the dimension of the nullspace. In other words, that is the number of vectors you need to span it.
<_shellcode_> ok, but isn't rank the number of NON-zero rows?
<asphyxia> yeah.
<asphyxia> that's why the total number of rows is the rank plus the nullity. It is nice to keep that in mind.
<_shellcode_> i don't know the term nullity
<asphyxia> nullity is the dimension of the nullspace
<asphyxia> that means, the number of vectors you need to span it.
<asphyxia> As I see it, you are right on spanning the nullspace with only one vector.
<_shellcode_> alright, this makes more sense now
<asphyxia> The spanning set is just the set of that vector v, ergo {v}.
<asphyxia> remember, if you're asked for the spanning set, remember to specify it as a set with braces!
<_shellcode_> ah ok, good reminder
<me22> isn't it "a" spanning set?
<gzl> yes
<asphyxia> gzl: if you have set X and a permutation o, and you define a_1 = a, a_2 = o(a_1),...,a_{i+1} = o(a_i), then what do you call the set B_a(o)={a_1, a_2, a_3, ...}.
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