Finding basis for subspace

[sallies]

Homework Statement

find a basis for the subspace R^5 that consists of all the vectors of the form [(b-c), (d-2b), (4d), (c-2d), (6d+2b)]

Homework Equations

The Attempt at a Solution

the only solution I can think of is e1, e2, e3, e4, e5... I don't think it's that simple though... would appreciate any input on this question. Thanks!

 

[Mark44]

a = b - c
b = -2b   + d
c =         4d
d =      c - 2d
e = 2b     + 6d

A vector in this subspace is a linear combination of three vectors, which you can pick out of the equations above.