Imagine trying to solve a 1,800,000 by 900,000 system of linear equations. This was the problem facing NAD (North American Datum) geologists to establish accurate GPS points on the Earth’s surface. The system is obviously over determined and thus has no solution in the ordinary sense, but it does have a least square solution (where the normal equations are a 928,735 by 928,735 system of linear equations!) 
To get an idea of how to solve these type of large problems (and to use software to assist in the solution process), answer the following questions:
1. Verify the example given above by working out the matrix operations (multiplications, etc.).
2.Given the US population data set “PopulationData.csv” , determine a linear regression solution for the data. The data is for the US (total) population from 1950 to 2017 shifted to start in 1950 (that is, “year 0” is the year 1950). Do this by doing the following:
a.Plot the data (scatter plot) using some plotting software or online tool. b.  Set up and solve (again, using software) the normal equations for the linear regression (least square) function. c.  Give the equation of the resulting line and plot it with the given data
3. From calculus, we learned that the basic population growth model (where we assume the rate of growth is proportional to the population size) is given by
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