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(f1,f2,f3) = 


                = 
Taking x common form 1st Row
               = 
              = 



Now, 


                                = x(24x^4 - 18x^4)
                                = 6x^5 which is not equal to o
Therefore, f1, f2, f3 are Linearly Independent.

Here is the Video for any doubt





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