Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

KonradZuse

  • 2 years ago

Find a basis for the null space of A.

  • This Question is Closed
  1. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest @asnaseer @CliffSedge

    1 Attachment
  3. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  4. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  6. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  7. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    woah... LOL

  8. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  9. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  10. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  11. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  12. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  13. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    row reduce, what do you get?

  14. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  15. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, it's not

  16. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  17. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  18. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  19. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  20. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh I found it.... :)

  21. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  22. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    HJHAHAH

  23. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  24. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  25. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my eyes they burn.... :)

  26. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you're so smart TT :Pe

  27. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  28. KonradZuse
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah yeah yeah!

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.