Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

BenBlackburn Group Title

Let V be the span of the vectors (1,3,-1,2),(-1,2,-1,-4). Express V as the solution set of a homogenous linear system.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. colorful Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not quite sure I understand the question...

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

    I was having the same issue. i dont even know where to start lol

    • 2 years ago
  3. colorful Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it's asking to express the general form I suppose?\[A\vec x=\vec0\]and we have\[A=\left[\begin{matrix}1&-1\\3&2\\-1&-1\\2&-4\end{matrix}\right]\]and\[\vec x=\left[\begin{array}~x_1\\x_2\\x_3\\x_4\end{array}\right]\]but what does it want us to write exactly?

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

    oh that matrix is sideways I think

    • 2 years ago
  5. colorful Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no, it's just that the \(\vec x\) is 2 rows long\[A\vec x=\vec0\]and we have\[A=\left[\begin{matrix}1&-1\\3&2\\-1&-1\\2&-4\end{matrix}\right]\]and\[\vec x=\left[\begin{array}~x_1\\x_2\end{array}\right]\]but what does it want us to write?

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

    ummm i have no clue

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

    well, the solution set is supposed to be the vector space, so we need to write the set of all solution in set notation somehow it seems

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

    but it says the "homogeneous solution" so I guess let's first solve the above

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

    but I'm thinking maybe homogeneous doesn't mean =0

    • 2 years ago
  10. BenBlackburn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhh ya i think it does mean =0

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

    so then I think that the span is the set\[V=\{\vec x:A\vec x=\vec0\}\]where\[A=\left[\begin{matrix}1&-1\\3&2\\-1&-1\\2&-4\end{matrix}\right]\]

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

    not sure how exactly they want you to state it, but the set of all vectors that solve that system seems to be the vector space they are talking about

    • 2 years ago
  13. BenBlackburn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so its just saying to express the V as the solution set of a homogenious system?

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

    usually the span of those vectors is the set of all linear combinations of those vectors, so you if not for the word "homogenous" I would say the span is just\[S=\{c_1\langle1,3,-1,2\rangle\},c_2\langle-1,2,-1,4\rangle\}\]

    • 2 years ago
  15. colorful Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    typo, I meant \[S=\{c_1\langle1,3,-1,2\rangle,c_2\langle-1,2,-1,4\rangle\}\]

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

    hard to know what they want you to write exactly imo

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

    correct i definitely see that

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

    but I don't think what I just wrote is "homogenous"

    • 2 years ago
    • Attachments:

See more questions >>>

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.