Let be a matrix such that

and let be endormorphism associated to with respect to some base of . Find the correct statement.

Question

Let    be a matrix such that 
  
 and let    be endormorphism associated to    with respect to some base of   . Find the correct statement.

Answer

The characteristic polynomial     of the matrix    is divisible by   .

Answer

The linear system    has solutions for any

Answer

The matrix    has rank   .

Answer

The matrix    has non-zero determinant.

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