# Homework Help: Lin Alg - Find the basis and dimension

1. Jul 19, 2010

### jinksys

Find the basis and dimension of the following homogeneous system:
Code (Text):

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?

2. Jul 19, 2010

### vela

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

3. Jul 19, 2010

### jinksys

Thanks for the help!