Symmetric matrix

6. ( 6 pts ) Consider the following symmetric matrix: 1 1 A=1 11 1 1 1 Compute the spectral decomposition of A = QAQwhere Q is an orthogonal matrix and A a diagonal matrix.2. A Markov chain with state space {1, 2, 3} has transition probability matrix 0.6 0.3 0.1 [Pa = 0.3 0.3 0.4 0.4 0.1 0.5 (a) Is this Markov chain irreducible? Is the Markov chain recurrent or transient? Explain your answers. (1)] What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (0) Consider a general three-state Markov chain with transition matrix P11 P12 P13 1?: 1021 1022 p23 P31 P32 P33 Give an example of a specic set of probabilities pm; for which the Markov chain is not irreducible (there is no single right answer to this, of course l]. Determine if the following items represent an example of positive economics or normative economics. The richest 1% of Americans should pay more taxes than the rest of the 99%. O Positive Economics O Normative Economics O A decrease in the supply of coconut will increase the price of German Normative Economics chocolate cake, a good which requires coconut shavings as a key ingredient O Positive Economics The higher the minimum wage, the higher the price of goods and services Normative Economics is likely to bo. OO Positive Economics Social welfare spending in Sweden occupies too large a portion of the O Positive Economics national budget. O Normative EconomicsMatch the assumptions to the theory Hold and drag to reorder Keynesian Sticky wages Economics Say's Law =Classical Economics F. A. Hayek Classical Economics Laissez Faire Policy E Classical Economics Recessionary Gap and Keynesian Long Run Equilibrium Economics