Suppose \(v₁, \ldots, vₘ\) are linearly independent vectors in \(V\), and \(w ∈ V\). Prove that \(\text{dim}(\text{span}(v₁ - w, v₂ - w, \ldots, vₘ - w)) ≥ m - 1\).
A. \(\text{dim}(\text{span}(v₁ - w, v₂ - w, \ldots, vₘ - w)) = m\)
B. \(\text{dim}(\text{span}(v₁ - w, v₂ - w, \ldots, vₘ - w)) ≤ m\)
C. \(\text{dim}(\text{span}(v₁ - w, v₂ - w, \ldots, vₘ - w)) = m - 1\)
D. \(\text{dim}(\text{span}(v₁ - w, v₂ - w, \ldots, vₘ - w)) > m - 1\)