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http://upload.wikimedia.org/math/5/8/2/582b41cd88284564c46e711cbbca55fa.png

http://en.wikipedia.org/wiki/System_of_linear_equations#Homogeneous_systems

A general solution to some linear system is

a particular solution (P) + a homogeneous solution (H)

My question:

is this also true for any multiple of the particular solution +/ any multiple of the homogenous solution? Or does it have to be P + H or P-2H, etc.?

Thank you!