in Linear Algebra
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While solving linear homogeneous equation do we check rank of A or rank of (A!B) ?
in Linear Algebra
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We have to check both Rank[A] as well as Rank[A:B] (the augmented matrix)

  • If Rank[A] = Rank[A:B], then only the system is consistent

Now check for what kind of solution it has:

i) If Rank[A] = Rank[A:B] = n (number of unknowns), then a unique solution exists

ii) If Rank[A] = Rank[A:B] $<$ n, then infinite number of solutions exist

  • If Rank[A] $\neq$ Rank[A:B], then the system is inconsistent i.e. no solution exists
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But in case of homogeneous Rank(A)=(Rank(A:B) always as i think.I think you gave inhomogeneous.I am asking for homogeneous
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Oh sorry! I didn't read it!

And yes, in case of homogeneous system Rank(A)=(Rank(A:B) is always true hence the system is never inconsistent.

X=0 is always a solution (trivial solution)
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