Suppose that the Wronskian of two functions f1t and f2t is g

Suppose that the Wronskian of two functions f_1(t) and f_2(t) is given by W(t) = t^2 - 4 = det [f_1(t) f_2(t) f_1\'(t) f_2\'(t)] Even though you don\'t know the functions f_1 and f_2 you can determine whether the following questions are true or false. The vectors (f_1(4),f_1\'(4)) and (f_2(4),f_2\'(4)) are linearly independent ? The vectors (f_1(0),f_1\'(0)) and (f_2(0),f_2\'(0)) are linearly independent The functions f_1 and f_2 are linearly independent. The vectors (f_1(-2)),f_1\'(-2)) and (f_2(-2)),f_2\'(-2)) are linearly independent The equations af_1(2) + bf_2(2) = 0 af_1\'(2) + bf_2\'(2) = 0 have more than one solution.

Solution

1. True

2. True

3. True

4. False

5. False