Find a basis for the null space of A.

- KonradZuse

Find a basis for the null space of A.

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- KonradZuse

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

- KonradZuse

@TuringTest @asnaseer @CliffSedge

##### 1 Attachment

- KonradZuse

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- KonradZuse

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

- 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

- KonradZuse

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

- KonradZuse

woah... LOL

- KonradZuse

1 4 5 2
2 1 3 0
-1 3 2 2

- KonradZuse

now do I have to augment it with the 0 column-vector?

- TuringTest

go ahead and row reduce it as much as you can
brb, gotta go to get dinner

- KonradZuse

the book does 2 eq's which is really annoying....

- KonradZuse

how they would both be the same, so it seems like it's not an augmented matrix....

- TuringTest

row reduce, what do you get?

- KonradZuse

OOOOOOOOOOOOOOOo There's a Null Space/Nullity thing on Maple hehehe. I guess it isn't augmented then :D

- TuringTest

no, it's not

- KonradZuse

1 0 1 -2/7
0 1 1 4/7
0 0 0 0

- KonradZuse

now I actually found something that says the num space is the subspace of vectors x satisfying A. x = 0

- KonradZuse

it shows the null space as
2/7
-4/7
0
1
then another column matrix next to it.
-1
-1
1
0..

- KonradZuse

Is there a matrix thing in the equations..... This is stupid writing it out like this :P.

- KonradZuse

oh I found it.... :)

- TuringTest

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

- KonradZuse

HJHAHAH

- KonradZuse

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

- 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

- KonradZuse

my eyes they burn.... :)

- KonradZuse

you're so smart TT :Pe

- 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

- KonradZuse

yeah yeah yeah!

Looking for something else?

Not the answer you are looking for? Search for more explanations.