Results 1 to 12 of 12

Math Help - A couple of questions

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    23

    A couple of questions

    1. Let v1 = [-3; 3; -4], v2 = [3; -2; 8] and y = [-12; 9; h]

    For what value of is in the plane spanned by and ?


    2. Which of the following sets are subspaces of ?

    A.
    B. arbitrary number
    C. arbitrary number
    D. arbitrary number
    E.
    F.

    Check all that apply.

    Sort of desperate for help

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by elven06 View Post

    2. Which of the following sets are subspaces of ?

    A.
    B. arbitrary number
    C. arbitrary number
    D. arbitrary number
    E.
    F.

    Check all that apply.

    Sort of desperate for help

    Thanks in advance!
    A. \alpha=-1
    B. I think you can do this one.
    C.
    D.You try.
    E. What about \alpha=2
    F. (1,0,0)+(0,1,0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Quote Originally Posted by Drexel28 View Post
    A. \alpha=-1
    B. I think you can do this one.
    C.
    D.You try.
    E. What about \alpha=2
    F. (1,0,0)+(0,1,0)
    I'm confused
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by elven06 View Post
    I'm confused
    By what?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Quote Originally Posted by Drexel28 View Post
    By what?

    your explanation
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by elven06 View Post
    your explanation
    ...which part?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Quote Originally Posted by Drexel28 View Post
    ...which part?

    I guess I still have no idea what to do in order to see which make it true... Your hints are tough to make use of given I have a weak grasp of the concept
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by elven06 View Post
    I guess I still have no idea what to do in order to see which make it true... Your hints are tough to make use of given I have a weak grasp of the concept
    Ok. That's fine. So let's go through an example, ok?

    A subspace must be closed under scalar multiplication and vector addition. So, for example F. is not a subspace since if we let V=\left\{(x,y,z)\in\mathbb{R}^3:x+y+z=1\right\} then surely (1,0,0)\in V,(0,1,0)\in V but since (1,0,0)+(0,1,0)=(1,1,0) has the quality that 1+1+0\ne 1 we see that (1,0,0)+(0,1,0)\notin V. But, this HAS to happen in a subspace. So, V is not a subspace.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Quote Originally Posted by Drexel28 View Post
    Ok. That's fine. So let's go through an example, ok?

    A subspace must be closed under scalar multiplication and vector addition. So, for example F. is not a subspace since if we let V=\left\{(x,y,z)\in\mathbb{R}^3:x+y+z=1\right\} then surely (1,0,0)\in V,(0,1,0)\in V but since (1,0,0)+(0,1,0)=(1,1,0) has the quality that 1+1+0\ne 1 we see that (1,0,0)+(0,1,0)\notin V. But, this HAS to happen in a subspace. So, V is not a subspace.

    Great, so I think I understand that B definitely is because you can multiply by any scalar to remain in R.

    I'm thinking that C is also true because 0 is in R as well.

    I'm not sure about others :/
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by elven06 View Post
    Great, so I think I understand that B definitely is because you can multiply by any scalar to remain in R.

    I'm thinking that C is also true because 0 is in R as well.

    I'm not sure about others :/
    It has to satisfy ALL the properties of a subspace. Do you know them all?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Quote Originally Posted by Drexel28 View Post
    It has to satisfy ALL the properties of a subspace. Do you know them all?
    I must not..
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Feast your eyes.
    Quote Originally Posted by elven06 View Post
    I must not..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with a couple of questions
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 25th 2011, 10:27 AM
  2. [SOLVED] A couple questions...Help please.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 24th 2010, 06:05 PM
  3. A couple of Questions.
    Posted in the Geometry Forum
    Replies: 5
    Last Post: April 8th 2009, 10:54 AM
  4. a couple of questions...thanks
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 12th 2008, 09:18 PM
  5. Couple of questions
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 20th 2007, 06:28 AM

Search Tags


/mathhelpforum @mathhelpforum