Each year, 10% of employed people are losing their jobs, and half of the unemployed workers find jobs. Let us denote by et the number of employed workers in year t and by ut the number of unemployed workers in year t. 1. Show that number of employed and unemployed workers in year t+1 can be calculated as t+1 3: |: ] : A[ ,where A is a square matrix. 'Urt+1 \"Ur What is the matrix A? 2. Calculate the eigenvalues of matrix A The economy is said to reach a steady state when the number of employed people and the number of unemployed people is constant. That is, A [Bt+1] [fit] a A : : ,where e and ut+1 t \"a\" A u are the steady state values of employment and unemployment. 3. What is the connection between the vector A E and matrix A? "U. 4. Calculate the steady state value of the A '11- unemployment rate, \"U: : . e l u 5. What is the "definiteness" of the quadratic form 8x12 + ?xp_2 - 3x32 - oxixg + 4x1x3 - 2x2x3