Show by Wronskian that x, x^3, x^4 are Linearly Independent if x is non-zero.
Let f1(x) = x, f2(x) = x^3, f3(x) = x^4 f'1(x) = 1, f'2(x) = 3x^2 f'(x) = 4x^3 f"1(x) = 0, f"2(x) = 6x, f"3(x) = 12x^2 W( f 1, f 2, f 3) = = Taking x common form 1st Row = = Now, = x(24x^4 - 18x^4) = 6x^5 which is not equal to o Therefore...