Math 300
Laboratory 1 — Systems of Linear Equations
Due Tuesday, September 8, 2009 – 10 points
Names:
You may use books and notes but please work on this lab with your partner only. You must show all
work. Sentences explaining what you are doing are very important.
Your lab should be written entirely as a Derive document. Your document should be a combination
of sentences that explain what you are doing and Derive computations. To enter the text after a given
expression, highlight the expression and click on the Insert Text button. Do not do any computations by
hand. For example, to reduce a matrix A, use Derive command row_reduce(A).
Every group submits one report.
Read about “Polynomial Curve Fitting” in Section 1.3 (pages 29–33).
1. Consider the following six points in the plane: .4; 2/,.2; 4/,.1; 3/,.1; 2/,.2; 4/,.5; 1/.
(a) Find a polynomial yDa0Ca1xCa2x2Ca3x3Ca4x4Ca5x5of degree 5whose graph
passes through all these points. Show all work. (Use Example 2 on page 30 as a model.)
(b) Use DERIVE to plot the points and your fifth-degree polynomial in the same coordinate sys-
tem. Make sure that the graph passes through all six points. Select a suitable range so that the
points and curve are clearly visible: in 2D-plot window use Set/Plot Range/Minimum/maximum.
To plotthe points,enter them as the 62matrix Œ4;2I2;4I:::I5; 1 and plot in 2D-plot
window. In that window, select Options/Display/Points and click on Large so that the points
would be clearly visible.
2. The sales (in billions of dollars) for Wal-Mart stores from 2000 to 2007 are shown in the table
below. Year 2000 2001 2002 2003 2004 2005 2006 2007
Sales 191.3 217.8 244.5 256.3 285.2 312.4 346.5 377.0
(a) Set up a system of equations to fit the data for the years 2000–2007 to a seventh-degree
polynomial model. To avoidworking with large numbers, represent the year 2000 by xD0,
2001 by xD1,:::,2007 by xD7.
(b) Solve the system and write down your polynomialof degree 7.
(c) Use DERIVE to plot your polynomial and all points for the years 2000-2007 in the same
coordinate system. The graph should pass through all eight points. Select the x-range as
1x9and a suitable y-range so that the curve and the points are clearly visible.
(d) Use your model to predict Wal-Mart sales in the years 1999 and 2008. Are those reasonable
predictions? Explain.
Show all work.