For a real \(4 \times 3\) matrix \(M\) and the standard basis \(\{e_1,e_2,e_3\}\) of \(\mathbb{R}^3\), which of the following statements is/are true?
(I) If \(\text{rank}(M)=1\), then \(\{Me_1,Me_2\}\) is a linearly independent set in \(\mathbb{R}^4\).
(II) If \(\text{rank}(M)=2\), then \(\{Me_1,Me_2\}\) is a linearly independent set in \(\mathbb{R}^4\).
(III) If \(\text{rank}(M)=3\), then \(\{Me_1,Me_2\}\) is a linearly independent set in \(\mathbb{R}^4\).