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KonradZuse
 2 years ago
Find a basis for the null space of A.
KonradZuse
 2 years ago
Find a basis for the null space of A.

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KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0My book says that the null space is the solution space of Ax = b when b = 0. The example in the book shows this...

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0@TuringTest @asnaseer @CliffSedge

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0Do I just solve it and that's all...?

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0I'm also a bit confused how they got the column matrix's filled out... Maybe that's my issue...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1pretty much, yeah just solve it and rewrite each variable as a new vector, i.e. one for r, one for s, and one for t

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0hmm okay maybe this is easier than I'm thinking let me try it. My example is A = (Matrix(3, 4, {(1, 1) = 1, (1, 2) = 4, (1, 3) = 5, (1, 4) = 2, (2, 1) = 2, (2, 2) = 1, (2, 3) = 3, (2, 4) = 0, (3, 1) = 1, (3, 2) = 3, (3, 3) = 2, (3, 4) = 2})); print(`output redirected...`); # input placeholder

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.01 4 5 2 2 1 3 0 1 3 2 2

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0now do I have to augment it with the 0 columnvector?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1go ahead and row reduce it as much as you can brb, gotta go to get dinner

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0the book does 2 eq's which is really annoying....

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0how they would both be the same, so it seems like it's not an augmented matrix....

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1row reduce, what do you get?

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0OOOOOOOOOOOOOOOo There's a Null Space/Nullity thing on Maple hehehe. I guess it isn't augmented then :D

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.01 0 1 2/7 0 1 1 4/7 0 0 0 0

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0now I actually found something that says the num space is the subspace of vectors x satisfying A. x = 0

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0it shows the null space as 2/7 4/7 0 1 then another column matrix next to it. 1 1 1 0..

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0Is there a matrix thing in the equations..... This is stupid writing it out like this :P.

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0oh I found it.... :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1setting up matrices with latex is a pain, you are doing it the easy way

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0\[\left(\begin{matrix}2/7 \\4/7\\ 0\\ 1\end{matrix}\right), \left(\begin{matrix}1 \\1\\ 1\\ 0\end{matrix}\right)\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1yes, you get that from 1 0 1 2/7 x1+r2/7s=0>x1=r+2/7s 0 1 1 4/7 x2+r+4/7s=0>x2=r4/7s collect the r's in one vector and the s's in another

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0my eyes they burn.... :)

KonradZuse
 2 years ago
Best ResponseYou've already chosen the best response.0you're so smart TT :Pe

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1first row of your matrix reduced: 1 0 1 2/7 this is the same as the equation x1+r2/7s=0 which leads to x1=r+2/7s and thanks, but I need to get better at computer stuff now, so maybe I'll need your help sorry, back in 15
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