Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements:
$S1: M $ has $4$ linearly independent eigenvectors.
$S2: M$ has $4$ distinct eigenvalues.
$S3: M$ is non-singular (invertible).
Which one among the following is TRUE?
- $S1$ implies $S2$
- $S1$ implies $S3$
- $S2$ implies $S1$
- $S3$ implies $S2$