Linear algebra

  • Thread starter blinder
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  • #1
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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)
 

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  • #2
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Is the matrix [itex]N = (0)[/itex] singular? Does [itex]Nx = b[/itex] have infinitely many solutions if b is nonzero?
 
  • #3
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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.
 
  • #4
mathwonk
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or you might say the question is meaningless since you do not quantify the letter "b".
 

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