^{4}that satisfies the following equation:

-3x

_{1}-5x

_{2}-8x

_{3}-4x

_{4}=0

The basis should be three vectors with 4 components each

I tried V

_{1}as (-3,0,0,0), V

_{2}as (0,-5,0,0), V

_{3}as (0,0,-8,-4). But that was incorrect.

Wouldn't the subspace for this be the Vectors (-3,0,0,0), (0,-5,0,0), (0,0,-8,0), (0,0,0,-4) or any multiple? I feel like the basis would have to be in R

^{4}because it is linearly independent with 4 vectors.