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If x₀ is one particular solution, all solutions have the form x₀+z where z is any vector in the kernel of A (i.e., Az=0). The solution set is an affine translate of the kernel and does not necessarily pass through the origin.
Conditions: The system Ax=b is consistent.; x₀ is a specific solution such that Ax₀=b.
If x₀ is one particular solution, all solutions have the form x₀+z where z is any vector in the kernel of A (i.e., Az=0). The solution set is an affine translate of the kernel and does not necessarily pass through the origin.
Conditions: The system Ax=b is consistent.; x₀ is a specific solution such that Ax₀=b.