please show work and explain my lecture on this was super unhelpful

Part A)

Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions:

y=e^(4x) and z=e^(2x)

Think of the corresponding vector solutions ₁ and ₂ and use the Wronskian to show that the solutions are linearly independent

Wronskian=det[ should be a 2 by 2 matrix] = ?

These solutions are linearly independent because the Wronskian is [zero or non zero] for all x.

Part B)

Use the Wronskian to determine whether the functions y₁=six(3x) and y₂=cos(6x) are linearly independant

Wronskian=det[ should be a 2 by 2 matrix] = ?

These functions are linearly independent because the Wronskian is nonzero for [some/all] values of x.