Dimension of space vectors

Question

What is the dimension of the space of vectors in R^5 having the form of: (a-3b, b-a, a+2b, a, b)? Please show a step by step solution.

Answer 1

(a-3b, b-a, a+2b, a, b) = a(1, -1, 1, 1, 0) + b(-3, 1, 2, 0, 1)

Since any vector in the subspace can be expressed as a linear combination of the 2 linearly independent vectors (1, -1, 1, 1, 0) and (-3, 1, 2, 0, 1), those 2 vectors form a basis of the subspace..

So, the subspace is of dimension 2.