Results 1 to 2 of 2

Math Help - Column Space and Linear Combinations Question

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    16

    Column Space and Linear Combinations Question

    I am stuck on how to work out this question.

    1) In each case determine whether b is in the column space of A, and if so, express b as a linear combination of the column vectors A.



    My answer so far to (b):



    Is someone able to let me know if this column space is correct?

    My main question: If so, how am I supposed to find out if b is in the column space?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    The column space is just the space spanned by the columns of A. (But in this problem they also form a basis for the column space because they're linearly independent.)

    If b is in the column space of A, then there exits an  \alpha ,  \beta and  \gamma such that

     \alpha \left(\begin{array}{c} 1 \\ 9 \\ 1\end{array}\right) + \beta \left(\begin{array}{c} -1 \\ 3\\ 1\end{array}\right) + \gamma \left(\begin{array}{c} 1 \\ 1 \\ 1\end{array}\right) = \left(\begin{array}{c}-5 \\ 1\\ -1\end{array}\right)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on null space/column space/row space of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 1st 2011, 01:47 PM
  2. Question about column space
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 16th 2011, 07:36 AM
  3. Replies: 1
    Last Post: January 14th 2011, 09:51 AM
  4. show column space of A^2 contained in column space of A
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 22nd 2010, 10:18 AM
  5. column space, null space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: August 31st 2008, 09:49 AM

Search Tags


/mathhelpforum @mathhelpforum