MADE EASY

Question

The Necessary condition to diagonalize a matrix is that

A)  ITS all eigen values should be distdist

B) its eigen vectors should be indeindepent

C) its eigen values should be real

D) matrix is non singular

Comments

$A$.

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B..................

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all eigen values are distinct than  then corresponding eigen vectors are independent vector.
 

if all eigen vectors are independent then matrix is diagonalizable

hence i think both a and b both option are correct please correct me if i wrong

Answer 1

B is the correct option.

As for diagonalization eigen vectors should be independent.

Same eigen values can even give independent eigen vectors.example try to find eigen values and vectors of identity matrix. So it can be diagonalised so A is not always true.