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e, and constraint inequalities do not affect the dimension. For which of the following domains does the rule of thumb give the wrong answer? The set of (x, y) satisfying x² + y² ≤9 and x + y > 0. The set of (x, y, z) satisfying a² + 2y² + 3z² = 10000 and x + y + z = 1. The set of (x, y, z) satisfying x+y+z= 0, 3x + 4y + 5z = 0, and 6x + 7y + 8z = 0. The set of (x, y) satisfying x² - y² = 25 and x > 0.

e, and constraint inequalities do not affect the dimension. For which of the following domains does the rule of thumb give the wrong answer? The set of (x, y) satisfying x² + y² ≤9 and x + y > 0. The set of (x, y, z) satisfying a² + 2y² + 3z² = 10000 and x + y + z = 1. The set of (x, y, z) satisfying x+y+z= 0, 3x + 4y + 5z = 0, and 6x + 7y + 8z = 0. The set of (x, y) satisfying x² - y² = 25 and x > 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A rule of thumb says that if a domain is defined by e constraint equations in n variables, then the dimension of the domain is n - e, and constraint inequalities do not affect the dimension. For which of the following domains does the rule of thumb give the wrong answer? The set of (x, y) satisfying x² + y² ≤ 9 and x + y > 0. The set of (x, y, z) satisfying x² + 2y² + 3z² 10000 and x+y+z=1. The set of (x, y, z) satisfying x + y + z = 0, 3x + 4y + 5z The set of (x, y) satisfying x² - y² = 25 and x > 0. 0, and 6x + 7y + 8z = 0.
Transcribed Image Text:A rule of thumb says that if a domain is defined by e constraint equations in n variables, then the dimension of the domain is n - e, and constraint inequalities do not affect the dimension. For which of the following domains does the rule of thumb give the wrong answer? The set of (x, y) satisfying x² + y² ≤ 9 and x + y > 0. The set of (x, y, z) satisfying x² + 2y² + 3z² 10000 and x+y+z=1. The set of (x, y, z) satisfying x + y + z = 0, 3x + 4y + 5z The set of (x, y) satisfying x² - y² = 25 and x > 0. 0, and 6x + 7y + 8z = 0.
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