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

derrick902 Group Title

How do you show that vector, x= (2,3,4)+ t1 (1,1,1) + t2 (1,2,3) is a subspace of R^n?

  • one year ago
  • one year ago

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

    Well for starters in order for a vector to be a subspace it must be linearly dependant

    • one year ago
  2. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Since ( 2,3,4)=(1,1,1)+(1,2,3), it follows that (2,3,4)+t1(1,1,1)+t2(2,3,4)=(t1+1)(1,1,1)+(t2+1)(2,3,4)

    • one year ago
  3. swissgirl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmmmm I would go about it just a drop differently

    • one year ago
  4. swissgirl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \left( \begin{array}{ccc} 2 & 1 & 1 \\ 3 & 1 & 2 \\ 4 & 1 & 3 \end{array} \right)\] I forgot the terms but basically x=(2+1t_1+1t_2)+(3+1t_1+2t_2)+(4+1t_1+3t_2) Now if you would row reduce this then you will see that this matrix is linearly dependant

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

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 3 & 1 & 2 \\ 4 & 1 & 3 \end{array} \right)\] 1/2R_1=R_1

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

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 0 &- {1 \over 2} & - {1 \over 2} \\ 4 & 1 & 3 \end{array} \right)\] 3R_1+R_2=R_2

    • one year ago
  7. swissgirl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 0 &1 & 1 \\ 4 & 1 & 3 \end{array} \right)\] -2R_2=R_2

    • one year ago
  8. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you are going to get all 0s in the first column, with one 1 in each of the second and third columns. Thats because (2,3,4)=1(1,1,1)+1(1,2,3).

    • one year ago
  9. swissgirl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 0 &1 & 1 \\ 0 & -2 & -2 \end{array} \right)\] -4R_1+R_3=R_3

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

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 0 &1 & 1 \\ 0 & 1 & 1 \end{array} \right)\] -1/2R_3=R_3

    • one year ago
  11. swissgirl Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \left( \begin{array}{ccc} 1 & {1 \over 2} & {1 \over 2} \\ 0 &1 & 1 \\ 0 &0 & 0 \end{array} \right)\] -1R_2+R_3=R_3 As you see the last row is just zeroes this means that this matrix is linearly dependant meaning that it is a subspace

    • one year ago
  12. derrick902 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks :)

    • 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.