Wronskian Suppose that f and g are differentiable functions on the unit interval I. The Wr...

Wronskian Suppose that f and g are differentiable functions on the unit interval I. The Wronskian of f and g is given by

Show that if W[f, g](t) ≠ 0 for all t in I, then f and g are linearly independent. HINT: If c1f(t) + c2g(t) = 0, then c1f′(t) + c2g′(t) = 0; use Cramer’s Rule to solve for c1 and c2.