M21001-HW1 - 1 Problem 4 Attempt to solve the system-x 1 +...

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MATH 21001 - Spring 2010 - Homework 1 Hassan Allouba Problem 1 Consider the following three systems where the coefficients are the same for each system, but the right-hand sides are different (this situation occurs frequently): 8 x - 16 y + 10 z = 1 | 0 | 0 , 12 x - 21 y + 12 z = 0 | 1 | 0 , 3 x - 4 y + 2 z = 0 | 0 | 1 . Solve all three systems at one time by performing Gaussian elimination on an augmented matrix of the form ± A | b 1 | b 2 | b 3 ² . Problem 2 Find angles α , β , and γ such that 2 sin α - cos β + 3 tan γ = 3 , 4 sin α + 2 cos β - 2 tan γ = 2 , 6 sin α - 3 cos β + tan γ = 9 , where 0 α 2 π , 0 β 2 π , and 0 γ < π . Problem 3 The following system has no solution: - x 1 + 3 x 2 - 2 x 3 = 1 , - 2 x 1 + 8 x 2 - 6 x 3 = 0 , - 3 x 1 + 15 x 2 - 12 x 3 = 0 , Attempt to solve this system using Gaussian elimination and explain what occurs to indicate that the system is impossible to solve.
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Unformatted text preview: 1 Problem 4 Attempt to solve the system-x 1 + 3 x 2-2 x 3 = 4 ,-2 x 1 + 7 x 2-5 x 3 = 9 ,-5 x 1 + 19 x 2-14 x 3 = 24 . using Gaussian elimination and explain why this system must have innitely many solutions. Problem 5 By solving a 3 3 system, nd the coecients in the equation of the parabola y = + x + x 2 that passes through the points (1 , 1), (2 , 2), and (3 , 0). Problem 6 Explain why a linear system can never have exactly two dierent solutions. Extend your argument to explain the fact that if a system has more than one solution, then it must have innitely many dierent solutions. 2...
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M21001-HW1 - 1 Problem 4 Attempt to solve the system-x 1 +...

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