Question

For k ∈ $\N$, let 0 = t0 < t1 < ⋯ < tk < tk+1 = 1. A function f : [0,1] → ℝ is said to be piecewise linear with nodes t1, … ,tk, if for each j = 1, 2, … , k + 1, there exist aj ∈ ℝ, bj ∈ ℝ such that
f(t) = aj + bjt for tj-1 < t < tj.
Let V be the real vector space of all real valued continuous piecewise linear functions on [0,1] with nodes $\frac{1}{4},\frac{1}{2},\frac{3}{4}$ . Then, the dimension of V equals ______________

Answer 1

The correct answer is 5.