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Find a basis for the null space of A.

Linear Algebra
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My book says that the null space is the solution space of Ax = b when b = 0. The example in the book shows this...
Do I just solve it and that's all...?

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I'm also a bit confused how they got the column matrix's filled out... Maybe that's my issue...
pretty 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
hmm 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
woah... LOL
1 4 5 2 2 1 3 0 -1 3 2 2
now do I have to augment it with the 0 column-vector?
go ahead and row reduce it as much as you can brb, gotta go to get dinner
the book does 2 eq's which is really annoying....
how they would both be the same, so it seems like it's not an augmented matrix....
row reduce, what do you get?
OOOOOOOOOOOOOOOo There's a Null Space/Nullity thing on Maple hehehe. I guess it isn't augmented then :D
no, it's not
1 0 1 -2/7 0 1 1 4/7 0 0 0 0
now I actually found something that says the num space is the subspace of vectors x satisfying A. x = 0
it shows the null space as 2/7 -4/7 0 1 then another column matrix next to it. -1 -1 1 0..
Is there a matrix thing in the equations..... This is stupid writing it out like this :P.
oh I found it.... :)
setting up matrices with latex is a pain, you are doing it the easy way
HJHAHAH
\[\left(\begin{matrix}2/7 \\-4/7\\ 0\\ 1\end{matrix}\right), \left(\begin{matrix}-1 \\-1\\ 1\\ 0\end{matrix}\right)\]
yes, you get that from 1 0 1 -2/7 x1+r-2/7s=0->x1=-r+2/7s 0 1 1 4/7 x2+r+4/7s=0->x2=-r-4/7s collect the r's in one vector and the s's in another
my eyes they burn.... :)
you're so smart TT :Pe
first row of your matrix reduced: 1 0 1 -2/7 this is the same as the equation x1+r-2/7s=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
yeah yeah yeah!

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