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Linear Algebra and Differential Equation.
Spring 2010
Assignment # 1
DUE DATE: 10 Feb , 20 10
Question#1: Find the currents through the resistors in the circuit shown below
Question# 2.: Solve the circuit shown below using system of linear equations. Note: Only Setup the equations, you need not to solve it.
Question#3: The chemical reaction below can be used in some industrial processes, such as production of arsene. Use exact arithmetic or rational format for calculations to balance this equation
Question#4: Suppose an economy consists of the coal, Electric (power), and Steel sectors, and the out put of each sector is distributed among the various sectors as shown in table, where the entries in a column represent the fractional parts of a sector’s total out put.
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Denote the prices of the total amount out puts of the Coal, Electric and steel sectors by respectively. If possible, find equilibrium prices that make each sector’s income match its expenditure. Distribution of Output from: Coal Electric Steel Purchased by .0 .4 .6 Coal .6 .1 .2 Electric .4 .5 .2 Steel
Question#5: Solve x+y+z= x-y-5z= 2x+3y+5z=
Question#6: In 2001 there were 110 million cell phone subscribers in the United States. This number grew to 128 million in 2002 and 141 million in 2003. Construct a model for these data by finding a quadratic function whose graph passes through point (1,110),(2,128) and (3,141). Use this model to estimate the number of subscribers in 2004 and 2005.
Question#7: For which values of a will the following system have no solutions? Exactly one solution? Infinitely many solutions?
Question#8: The flow of traffic at some round about is shown below:
Solve the system.
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