Read the following statements and find out which of these statements is/are correct:
I. If \(\alpha, \beta, \gamma\) are three linearly independent vectors in \(V(F)\) then \(\alpha+\beta\), \(\beta+\gamma\) and \(\gamma+\alpha\) are also linearly independent.
II. The vectors \(2x^3+x^2+x+1,\ x^3+3x^2+x-2,\ x^3+2x^2-x+3\) of \(V_4(R)\) are linearly independent.