Question

For k ∈ \(\N\), let 0 = t₀ < t₁ < ⋯ < t_k < t_k+1 = 1. A function f : [0,1] → ℝ is said to be piecewise linear with nodes t₁, … ,t_k, if for each j = 1, 2, … , k + 1, there exist a_j ∈ ℝ, b_j ∈ ℝ such that
f(t) = a_j + b_jt for t_j-1 < t < t_j.
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

Correct Answer: 5

The correct answer is 5.