Let M be a real 4 x 4 matrix. Consider the following statements:

S1 : M has 4 linearly independent eigen vectors.

S2 : M has 4 distinct eigen values.

S3 : M is non-singular (invertible).

Which one among the following is TRUE?

S1 implies S2

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S1 implies S3

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S2 implies S1

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S3 implies S2

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Solution

The correct option is C S2 implies S1
'Eigen vectors corresponding to distinct eigen values are linearly independent'

Hence $S_{2} \Rightarrow S_{1}$

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