Answers to Quizlet 5.1

1. Determine which of the following statements is true. (L is always a scalar, A a matrix, x a vector.)

• If Ax=Lx for some scalar L, then x is an eigenvector of A.

  Answer: False, the vector x must be non-zero.

• The eigenvalues of a matrix are on its main diagonal.

  Answer: False, this is however true if the matrix is a diagonal or (upper or lower) triangular matrix.

• A 2x2 matrix can have at most 2 eigenvalues.

  Answer: True.

2. Which of the following numbers are eigenvalues of the matrix with first row (1,-1,-1), second row (2,-1,4), (-3,1,-4)? Sqrt(x) denotes the square root of x.

Answer: Only -5 and (1/2)(1-Sqrt(5)) are actually eigenvalues. The third eigenvalue is (1/2)(1+Sqrt(5)).

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