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can anyone explain me 

  1.  how to find matrix if eigenvector and eigenvalues are given
  2. how to find eigenvalue when eigenvector and matrix is given
  3. how to find eigenvector when eigenvalue and matrix is given

totally confused in this thing please explain with example

1 Answer

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1.  use approach AX=$\lambda$X where A Will be the matrix present in ans options and as eigen values (lamda) is known, the matrix which satisfies is your ans

2. follow the same approach as above AX=$\lambda$X    OR MATRIX WILL BE sufficient to find eigen values.

3. MANY ways actually the above approach(same) OR You can use Cramers rule, Substitution (after converting it into row echelon form and it is based on rank).  if you need example please comment.

NOTE: X REPRESENTS EIGEN VECTOR

for example plzz https://gateoverflow.in/43968/isro-2013-33

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