Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra

  1. Apr 30, 2005 #1
    I had a hw problem and i was wondering if anyone could help me out with it. It is a true or fasle question that requires explanation whether true or false. It goes like this...If A is a singular n by n matrix, then A*x=b has infintely many solutions.(True or False)
     
  2. jcsd
  3. Apr 30, 2005 #2
    Is the matrix [itex]N = (0)[/itex] singular? Does [itex]Nx = b[/itex] have infinitely many solutions if b is nonzero?
     
  4. May 1, 2005 #3
    There are several case :

    b=0, then Ax=0 has infinitely many solution if det(A)=0

    b<>0 then it can have zero or an infinity of solution, depending on the determinants : [tex] det(b|_nA) [/tex]

    where [tex] b|_nA [/tex] means : the nth column of A is replace by b.

    So the answer is "true and false" because you don't specify enough the question.
     
  5. May 1, 2005 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    or you might say the question is meaningless since you do not quantify the letter "b".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear algebra
  1. Linear Algebra (Replies: 4)

  2. Linear Algebra (Replies: 1)

  3. Linear algebra (Replies: 2)

  4. Linear algebra (Replies: 2)

Loading...