Work out diagonalisation instantly with clear inputs, formula shown and shareable results.
A matrix is diagonalisable when its eigenvectors span the space, giving A = PDP⁻¹ with the eigenvalues on the diagonal of D. Distinct eigenvalues always guarantee this; a repeated eigenvalue may not.
Diagonalisation
A = PDP⁻¹, where the columns of P are eigenvectors and D holds the eigenvalues
The trace is 7 and determinant 6, so the eigenvalues are 6 and 1 — distinct, hence diagonalisable.
Powers become trivial: Aᵏ = PDᵏP⁻¹, and Dᵏ just raises each diagonal entry to the k.