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?

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.

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

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false

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