Question One a) Calculate the determinant of matrix A. Show your work in steps: A = 2013-2 - -2 1 3 2 -1 1 0 1 2 3 3-12 4 -3 1 1 3 2 0 b) Prove row linear independence is necessary and sufficient to column linear independence in the same matrix. c) Derive the inverse matrix of matrix B. Show your work in steps: [3 20 01 4 300 B = 0 0 6 5 LO 0 7 6]

Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?

Metropolitan Hospital has estimated its average monthly bed needs as N=1,000+9X where X=timeperiod(months);January2002=0 N=monthlybedneeds Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly seasonal adjustment factors have been estimated, using data from the past five years: Forecast Metropolitans bed demand for January, April, July, November, and December 2007. If the following actual and forecast values for June bed demands have been recorded, what seasonal adjustment factor would you recommend be used in making future June forecasts?

What is the difference between a series of economic data over time measured in nominal terms versus the same data series over time measured in real terms?