es x1 + 2x2 + x3 = 4, x2 x3 = 1, and x1 + 3x2 = 0 have at

Chapter 1, Problem 18E

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QUESTION:

PROBLEM 18EDo the three planes x1 + 2x2 + x3 = 4, x2 ? x3 = 1, and x1 + 3x2 = 0 have at least one common point of intersection? Explain.

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QUESTION:

PROBLEM 18EDo the three planes x1 + 2x2 + x3 = 4, x2 ? x3 = 1, and x1 + 3x2 = 0 have at least one common point of intersection? Explain.

ANSWER:

SOLUTIONStep 1Do the three planes , and have at least one common point of intersection Explain.This question is the same as asking if the linear system formed by these three equations is consistent.therefore we have to find the consistency of these equations.

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