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Sagot :
A is a 7x7 matrix with three eigen values. One eigenspace is two-dimensional and one of the other eigenspaces is three dimensional, then it is possible that A is not diagonalizable. The given statement is true.
There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is atleast one as there is atleast one non-zero eigen vector in them.
It is given that one of the eigen space has dimension 2 and other one has dimension 3.
A 7 x 7 matrix is diagonalizable if and only if the sum of the eigenspaces' dimension is 7. The given matrix is diagonalizable if and only if the third eigen space has dimension 2.
In A, if the sum of dimensions of eigenspace is not equal to the number of columns, then A is not diagonalizable.
To know more about eigenvalues:
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