Final answer:
To find a basis for the given vector space, substitute the given values and obtain a linearly independent set of vectors.
Step-by-step explanation:
To find a basis for the real vector space v = (a, b, c, d) ∈ R⁴: c = -6b, d = 2a, we can substitute the given values for c and d in terms of a and b.
Substituting c = -6b and d = 2a into the vector v, we get v = (a, b, -6b, 2a).
A basis for this vector space can be obtained by finding a linearly independent set of vectors that span the space. In this case, a possible basis is {(1, 0, 0, 0), (0, 1, -6, 0), (0, 0, 0, 2)}.