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

frx

Are the following set of vectors in R^4 linearly independent? \[\left\{ (1,0,2,-1),(1,2,-1,0),(1,1,0,-1) \right\}\] I want to get the set of vectors into matrixform but the "set" term confuses me a bit. Is this the right form? \[\left[\begin{matrix}1 & 0 &2&-1 \\1 & 2 &-1&0 \\1 & 1&0&-1\end{matrix}\right]=\left[\begin{matrix}0 \\ 0 \\0\end{matrix}\right]\] Or is it the other way around?

  • one year ago
  • one year ago

  • This Question is Closed
  1. Outkast3r09
    Best Response
    You've already chosen the best response.
    Medals 0

    you need to add a row o zeroes

    • one year ago
  2. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    Add a row of zeroes, what do you mean by that?

    • one year ago
  3. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1359278439800:dw|

    • one year ago
  4. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    That's how i ussualy write it, is that what you meant?

    • one year ago
  5. amoodarya
    Best Response
    You've already chosen the best response.
    Medals 1

    a(1,0,2,−1)+b(1,2,−1,0)+c(1,1,0,−1)=(0,0,0,0) they are independent if only a=b=c=0 multiply them and solve the system of equation

    • one year ago
  6. amoodarya
    Best Response
    You've already chosen the best response.
    Medals 1

    a+b+c=0 0a+2b+c=0 2a-b+0c=0 -1a+0b-c=0

    • one year ago
  7. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    \[a _{1}\left(\begin{matrix}1 \\0 \\ 2\\-1 \end{matrix}\right)+a _{2}\left(\begin{matrix}1 \\2 \\ -1\\0\end{matrix}\right)+a _{3}\left(\begin{matrix}1 \\1 \\ 0\\-1\end{matrix}\right)=\left(\begin{matrix}0 \\0 \\ 0\\0\end{matrix}\right)\] \[\left[\begin{matrix}1 & 1 & 1 \\0 & 2 & 1 \\ 2 & -1 & 0 \\-1 & 0 & -1 \end{matrix}\right]=\left(\begin{matrix}0 \\ 0 \\ 0 \\0\end{matrix}\right)\] \[\left[\begin{matrix}1 & 0 &0 \\0& 1 & 0 \\ 0&0&1 \\ 0&0&0\end{matrix}\right]=\left[\begin{matrix}0 \\ 0 \\0\\0\end{matrix}\right]\]

    • one year ago
  8. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    @amoodarya How should i interpret the reduced matrix, 000=0 but also 001=0 ?

    • one year ago
  9. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    So it can't really be a_3=t it must be a_3=0 and a_1=a_2=a_3=0 and the vectors are linearly independent, am I correct?

    • one year ago
  10. amoodarya
    Best Response
    You've already chosen the best response.
    Medals 1

    do you "rank of matrix" ?

    • one year ago
  11. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    Don't really know what rank of matrix is, will have to look it up.

    • one year ago
  12. frx
    Best Response
    You've already chosen the best response.
    Medals 0

    @amoodarya So the number of linearly independent vectors in the basis is three, so the rank should be three too, but what does this say about the dependent/independent case?

    • one year 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.