Results 1 to 3 of 3

Math Help - span, basis and dimension

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    204

    span, basis and dimension

    im having a little/big problem with the whole concept of span, basis and dimension
    eg. S = \{\left(\begin{array}{cc}a&b\\c&a\end{array}\right  ) \in V: a,b,c \in \Re \}
    how would i go about finding the span, the basis and the dimension of S?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1
    Quote Originally Posted by wik_chick88 View Post
    im having a little/big problem with the whole concept of span, basis and dimension
    eg. S = \{\left(\begin{array}{cc}a&b\\c&a\end{array}\right  ) \in V: a,b,c \in \Re \}
    how would i go about finding the span, the basis and the dimension of S?
    Is this a basis: \[<br />
\left\{ {\left( {\begin{array}{*{20}c}<br />
   1 & 0  \\<br />
   0 & 1  \\<br /> <br />
 \end{array} } \right),\,\left( {\begin{array}{*{20}c}<br />
   0 & 1  \\<br />
   0 & 0  \\<br /> <br />
 \end{array} } \right),\,\left( {\begin{array}{*{20}c}<br />
   0 & 0  \\<br />
   1 & 0  \\<br /> <br />
 \end{array} } \right)} \right\}~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    \begin{pmatrix}a & b \\ c & a\end{bmatrix}= \begin{pmatrix}a & 0 \\ 0 & a\end{pmatrix}+ \begin{pmatrix}0 & b \\ 0 & 0\end{pmatrix}+ \begin{pmatrix}0 & 0 \\ c & 0\end{pmatrix}

    It makes no sense to talk about finding the "span" of a vector space.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find a basis for span(T) as a subspace of R3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 12th 2010, 05:57 AM
  2. Dimension of span(Z)
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: January 17th 2010, 05:55 PM
  3. span and basis
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 11th 2009, 05:02 PM
  4. Vector Span and Dimension
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 1st 2008, 12:22 AM
  5. Dimension and Span of M_22
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 29th 2008, 06:50 AM

Search Tags


/mathhelpforum @mathhelpforum