Monthly Archives: May 2010

Linear Algebra and Its Applications, exercise 1.3.4

Exercise 1.3.4. Given the following system of equations: find a solution to the system, exchanging rows when necessary due to a zero pivot. Also, specify a coefficient for v in the third equation that would prevent elimination from being successful. … Continue reading

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Linear Algebra and Its Applications, exercise 1.3.3

Exercise 1.3.3. Given the following system of equations: find a solution to the system, and give the pivots. You can use a matrix to represent the system (including the right-hand side). Answer: We can represent the system as the following … Continue reading

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Linear Algebra and Its Applications, exercise 1.3.2

Exercise 1.3.2. Perform Gaussian elimination on the following system of equations: and find the resulting triangular system and the solution. Answer: The first pivot is 1. We subtract the first equation from the second and the third: The second pivot … Continue reading

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Linear Algebra and Its Applications, exercise 1.3.1

Exercise 1.3.1. Solve the following equation using Gaussian elimination: Answer: The first pivot is 2 (the coefficient of u in the first equation). We multiply the first equation by 2 (the coefficient of u in the second equation divided by … Continue reading

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Linear Algebra and Its Applications, exercise 1.2.13

Exercise 1.2.13. Given the equation x + 4y = 7 for a line in the x-y plane, find the equation for a line that is parallel to the first line and passes through the point (0, 0). The first line … Continue reading

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Linear Algebra and Its Applications, exercise 1.2.12

Exercise 1.2.12. We have two equations, x + y + z = 1 and x + y + z = 2. The first part of the exercise is to sketch the planes in 3-space associated with these two equations; I’m … Continue reading

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Linear Algebra and Its Applications, exercise 1.2.11

Exercise 1.2.11. Assume that we have the following system of two equations in two unknowns: Under what circumstances would this system have a set of solutions constituting an entire line in the x-y plane? Answer: Each of the equations corresponds … Continue reading

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