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You are given the equation of three planes which make an inconsistent system. П₁:5x - 3y + 4z - 9 = 0 П₂: 2x + y + 7z-6=0 П3: -15 x + 9y - 12z - 5 = 0 a) Explain what type of inconsistent system it is. Further, find the lines of intersection, if they exist, for each pair of planes. b) Describe any and all characteristics of the lines of intersection found in part a.

You are given the equation of three planes which make an inconsistent system. П₁:5x - 3y + 4z - 9 = 0 П₂: 2x + y + 7z-6=0 П3: -15 x + 9y - 12z - 5 = 0 a) Explain what type of inconsistent system it is. Further, find the lines of intersection, if they exist, for each pair of planes. b) Describe any and all characteristics of the lines of intersection found in part a.

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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You are given the equation of three planes which make an inconsistent system. П₁: 5x - 3y + 4z - 9 = 0 П₂: 2x+y + 7z-6=0 П3: -15 x + 9y - 12z - 5 = 0 a) Explain what type of inconsistent system it is. Further, find the lines of intersection, if they exist, for each pair of planes. b) Describe any and all characteristics of the lines of intersection found in part a.
Transcribed Image Text:You are given the equation of three planes which make an inconsistent system. П₁: 5x - 3y + 4z - 9 = 0 П₂: 2x+y + 7z-6=0 П3: -15 x + 9y - 12z - 5 = 0 a) Explain what type of inconsistent system it is. Further, find the lines of intersection, if they exist, for each pair of planes. b) Describe any and all characteristics of the lines of intersection found in part a.
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