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**[SOLVED] Finding a basis for a subspace**

## Homework Statement

We have a subspace U in R^3 defined by:

U = {(x_1 , x_2 ; x_3) | x_1 + 2*x_2 + x_3 = 0 }.

Find a basis for U.

## The Attempt at a Solution

We have the following homogeneous system:

(1 2 1 | 0).

From this I find the solution to be written as a*(2,1,0)^T + b(-1,0,1)^T, where a and b are arbitrary constants. From this I find

**three**linearly independant vectors.

Am I correct?