A is diagonalisable because it has 3 distinct eigenvalues, we can find 3 linearly independent eigenvectors by choosing one eigenvector from each eigenspace. Hence A is diagonlisable.
***Or just tell me how we know if a matrix is diagonalisable which is what i want to find out right now.
***Or just tell me how we know if a matrix is diagonalisable which is what i want to find out right now.
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A matrix is diagonalizable if the dimension of its eigenspace (that is the number of linearly independent eigenvectors it has) is equal to the number of vectors in the matrix itself. So if A is a 3 by 3 matrix. To be diagonalizable, it should have 3 linearly independent eigenvectors. This does not me that it should have 3 distinct eigenvalues as the same eigenvalue could give you two eigenvectors.