Question

at http://tutorial.math.lamar.edu/Classes/LinAlg/LinearIndependence.aspx
I don't understand the theorem1that how come the solutions are non-trivial?

Answer 1

Are you talking about the theorem that states: "A finite set of vectors that contains the zero vector will be linearly dependent"?

Answer 2

@KingGeorge YES

Answer 3

The equation they set up has at least one non-zero coefficient. In this case, it only has a single non-zero coefficient in front of the 0, but since it is non-zero, it's a non-trivial example.

Answer 4

OK

Answer 5

i guess trivial means simple solution, since cn=0 will satisfy the equation
and only trivial solution implies linear independence