Results 1 to 2 of 2

Math Help - Linear algebra. Showing n x n matrix has no inverse

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    11

    Linear algebra. Showing n x n matrix has no inverse

    If A is an n x n matrix, where n is an odd integer, which satisfies A^T=-A (ie its skew-symmetric). Show that A has no inverse...........i can understand why but i cant show it mathematically
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    Note that \det(^tA)=\det(A) and \det(aA)=a^n\det(A).
    Now, applying the determinant in the equality we have
    \det(^tA)=(-1)^n\det(A)\Rightarrow \det(A)=-\det(A)\Rightarrow 2\det(A)=0\Rightarrow\det(A)=0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 18th 2010, 09:48 AM
  2. Linear Algebra matrix problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 16th 2010, 03:59 AM
  3. linear algebra, rotation matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 21st 2009, 01:13 AM
  4. Linear Algebra Matrix Check
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 27th 2008, 09:07 AM
  5. matrix representation of linear algebra
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 30th 2008, 03:55 PM

Search Tags


/mathhelpforum @mathhelpforum