Suppose that the Wronskian of two functions f_1(t) and f_2(t) is given by W(t) =

Question

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.

Explanation / Answer

1. True

2. True

3. True

4. False

5. False

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