MathAlgebraLinear algebraMatrix decomposition

Diagonalizing matrices

Helping a colleague

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After much work, a physicist finds that his 8x8 matrix has 5 distinct eigenvectors. The geometric multiplicity of 3 of them is 1, while for the rest it is 2.
What can we tell the physicist about his matrix? Select the correct options

Select one option from the list

The matrix is diagonalizable, but it is not possible to construct D because exactly 8 are needed

The matrix is not diagonalizable because it needs to have more than 8 distinct eigenvalues.

The matrix is not diagonalizable because the sum of all geometric multiplicities is less than 8.

We cannot decide if the matrix is diagonalizable, we first have to check if the degree of the characteristic polynomial is exactly 8

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