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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?

  1. $S1$ implies $S2$
  2. $S1$ implies $S3$
  3. $S2$ implies $S1$
  4. $S3$ implies $S2$
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