To check whether a matrix is diagonalizable, follow these steps:

1. Define the Matrix: Provide the matrix you want to check for diagonalizability.

2. Find Eigenvalues:

   • Compute the eigenvalues of the matrix by solving the characteristic equation $\det(A - \lambda I) = 0$, where $\lambda$ are the eigenvalues.

3. Find Eigenvectors:

   • For each eigenvalue, find the corresponding eigenvector(s) by solving $(A - \lambda I)x = 0$.

4. Check Geometric and Algebraic Multiplicities:

   • The algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic equation.
   • The geometric multiplicity of an eigenvalue is the dimension of its eigenspace (the number of independent eigenvectors associated with it).

5. Conclusion:

   • A matrix is diagonalizable if, for every eigenvalue, the geometric multiplicity equals the algebraic multiplicity.
   • Alternatively, if the sum of the dimensions of the eigenspaces equals the size of the matrix (i.e., there are $n$ linearly independent eigenvectors for an $n \times n$ matrix), then the matrix is diagonalizable.

If you share the matrix, I can calculate all these steps for you and determine whether it is diagonalizable. Let me know if you'd like me to proceed!