Results 1 to 4 of 4

Math Help - Prove (or disprove) nonsingular in these two statements?

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    65

    Prove (or disprove) nonsingular in these two statements?

    A = n X n matrix, I is the identity matrix

    1) If A ^ 3 = O, then A - I is nonsingular

    2) If the product of k matrices A1 ... Ak is nonsingular, then each matrix Ai is non singular.


    Any thoughts?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    For # 1, I would take the equation

    A^{3}=0 and subtract I from both sides.

    For # 2, I would go with determinants.

    How do these ideas work for you?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    65
    Thanks, I can do it with the methods you suggested. However, the determinant section in my book comes after the section with these problems, so I'm kinda unsure if this method will be accepted. But thanks anyway.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well, for # 2, you could work with the row-reduced (upper triangular) versions of each matrix, and then focus on the last row-last column entry. You could do the same with # 1, after factoring.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. X~Exp(x,θ) prove or disprove that E[x^2]=2 (θ)^2
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 23rd 2010, 03:09 PM
  2. Prove or Disprove
    Posted in the Discrete Math Forum
    Replies: 52
    Last Post: March 24th 2010, 04:31 PM
  3. Prove or disprove
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 2nd 2009, 03:30 PM
  4. How do you prove these statements?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 3rd 2009, 12:47 PM
  5. Prove or Disprove
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: August 30th 2009, 08:47 AM

Search Tags


/mathhelpforum @mathhelpforum