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Let A be a 2 x 2 matrix with eigenvalues 1 = 2 and 12 = 0.5. Which of the following statements must be true?

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Let A be a 2 x 2 matrix with eigenvalues 1 = 2 and 12 = 0.5. Which of the following statements must be true? O The matrix A is a stochastic matrix (also known as a Markov matrix) O There is a nonzero vector x E R such that Ax = x O For all vectors x E R', either Ax = 2x or Ax = 0.5x O There is a one-dimensional vector subspace L C R" such that for any x E L, we have || Ax|| = 2|x||

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