For the matrix A = [ [2, 1], [0, 3] ], which statement about eigenvalues, eigenvectors and diagonalizability is correct?

For the matrix A = [ [2, 1], [0, 3] ], which statement about eigenvalues, eigenvectors and diagonalizability is correct?

• A. A has eigenvalues 2 and 3 with eigenvectors (1,0) for λ=2 and (1,1) for λ=3; A is diagonalizable.
• B. A has eigenvalues 2 and 3 with eigenvectors (1,0) for λ=3 and (0,1) for λ=2; A is diagonalizable.
• C. A has eigenvalues 2 and 3 with eigenvectors (1,0) for λ=2 and (0,1) for λ=3; A is not diagonalizable.
• D. A has eigenvalues 0 and 5; A is diagonalizable.

Answer: (A)