GATE-2018-ECE

Question

Let M be a real 4 × 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).
Whict one among the following is TRUE?
(a) S1 implies S2 (b) S2 implies S1
(c) S1 implies S3 (d) S3 implies S2

Note: Plz explain in detail why other options are incorrect.

Comments

@Arjun sir ,plz help

---

@Arjun sir, why option a is false? 

Answer 1

Should be option B. S2 implies S1.