State true/ false (with reason) For Linear Algebra

Question

Q1> Is it possible to have no Eigen vector corresponding to an Eigen value.

Q2> Rank of a matrix is equal to the number of non-zero Eigen values that matrix has.

{Explain with reason and counter example.}

Answer 1

answer 1)No it is not possible to have no eigen vector corresponding to eigen value

what do you mean by eigen value??? An eigenvalue represents the amount of expansion in the corresponding dimension. this expansion may be zero, smaller than 1, equal to 1, larger than 1, or even complex. But since there is an expansion, this amount of expansion must be represented by an eigenvalue.