Determine the number of solutions for a homogeneous system

anu914
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Hi all,

I would like to know how to determine the number of solutions for a Homogeneous system.
Ax = 0

A is a m*n matrix and x is a n*1 vector.

There are m equations and n unknowns. I'd like to know how to determine the number of solutions to this system.

Thank you in advance.
 
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First, thinking of the m rows as vectors, determine how many of them are independent (the "rank" of A). Call that number m'. By the "rank-nullity" theorem, the nullity, the dimension of kernal(A), will be n- m'. The number of (independent) solutions will be 1 if n- m'\le 0, and n- m' if it is greater than 0.
 
Thanks a lot for the answer...
 

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