Question

Show that any set containing a single non-null vector is a linearly independent.

Answer 1

in order for the set to be dependent, at least one vector must be writable as the sum/scaling of other vectors in the set, since these is only a single vector, there are no other vectors that can express it

Answer 2

Thank you but not getting the exact explanation.

Answer 3

it is vacuously true

Answer 4

or maybe just write down the definition. if your vector is non-zero v then given any linear combination
which in this case is just
\[av\] show that
\[av=0\] implies
\[a=0\] which it does because v is not the zero vector

Answer 5

Thanks