## KonradZuse 3 years ago Find a basis for the null space of A.

My book says that the null space is the solution space of Ax = b when b = 0. The example in the book shows this...

@TuringTest @asnaseer @CliffSedge

Do I just solve it and that's all...?

I'm also a bit confused how they got the column matrix's filled out... Maybe that's my issue...

5. TuringTest

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?

10. TuringTest

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....

13. TuringTest

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

15. TuringTest

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.... :)

21. TuringTest

setting up matrices with latex is a pain, you are doing it the easy way

HJHAHAH

$\left(\begin{matrix}2/7 \\-4/7\\ 0\\ 1\end{matrix}\right), \left(\begin{matrix}-1 \\-1\\ 1\\ 0\end{matrix}\right)$

24. TuringTest

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

27. TuringTest

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