Suppose that a is a square matrix with characteristic polynomial (λ - 3) 2 (λ - 6) 3 (λ + 1). (a) what are the dimensions of a? (give n such that the dimensions are n * n.) n = 6 correct: your answer is correct. (b) what are the eigenvalues of a? (enter your answers as a comma-separated list.) λ = 3,6,-1 correct: your answer is correct. (c) is a invertible?

Question

Krystal Velazquez

Mathematics

22 November, 02:56

Suppose that a is a square matrix with characteristic polynomial (λ - 3) 2 (λ - 6) 3 (λ + 1). (a) what are the dimensions of a? (give n such that the dimensions are n * n.) n = 6 correct: your answer is correct. (b) what are the eigenvalues of a? (enter your answers as a comma-separated list.) λ = 3,6,-1 correct: your answer is correct. (c) is a invertible?

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Allison Blackwell · Answer 1

The problem statement gives the correct answers for parts (a) and (b). The total number of roots of the characteristic polynomial is the dimension of the matrix: 6. The eigenvalues are the zeros of the characteristic polynomial, 3 (multiplicity 2), 6 (multiplicity 3), and - 1.

(c) The matrix is not invertible when one or more eigenvalues is zero. None of yours are zero, so the matrix is invertible.