Judgement of a linear system?

From: lucy (losemind_at_yahoo.com)
Date: 11/21/04 

Date: Sat, 20 Nov 2004 17:47:58 -0800

If the system can be written as a matrix multiply with the input vector in
discrete case; a integration of a kernel integrated against the input signal
in continuous case.

Then this system must be a linear system.

Is this statement true? Is it a sufficient and neccessary condition?