Lin Alg - Find the basis and dimension

[jinksys]

Find the basis and dimension of the following homogeneous system:

A =     |1 0 2| |x1|
        |2 1 3| |x2| = [0,0,0]
        |3 1 2| |x3|

My attempt:

Solving the coefficient matrix for RREF, I get the identify matrix.
So, x1=x2=x3=0 and the only solution is a trivial one.

Does that mean there is no basis(empty basis), or that the basis only contains the zero vector and has dimension zero?

 

[vela]

The dimension is equal to the number of vectors in a basis, so if the solution space is zero-dimensional, the basis is empty.

 

[jinksys]

The dimension is equal to the number of vectors in a basis, so if the solution space is zero-dimensional, the basis is empty.

Thanks for the help!