basis is Consider the endomorphism f of R whose matrix in the canonical A = 31...

 

  

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basis is Consider the endomorphism f of R whose matrix in the canonical A = 31 -20-2 1 3 3 5 1. Calculate the characteristic polynomial P; of f and the eigenvalues of f. 2. Prove that f is diagonalisable and find a basis of eigenvectors. 3. Check that Pf(f) = 0 and deduce the inverse of f. 4. For any n Z, calculate the matrix of f" in the canonical basis. basis is Consider the endomorphism f of R whose matrix in the canonical A = 31 -20-2 1 3 3 5 1. Calculate the characteristic polynomial P; of f and the eigenvalues of f. 2. Prove that f is diagonalisable and find a basis of eigenvectors. 3. Check that Pf(f) = 0 and deduce the inverse of f. 4. For any n Z, calculate the matrix of f" in the canonical basis.