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Using row reduction, show that the system of equations x+y+z=1 4x + 2y + z = 1 10x + 4y + z = 1 does not have a unique solution. In fact there is an infinite number of solutions, expressed in terms of a single parameter. Setting z = t, find an expression for x and y in terms of t. Verify (by substitution) that your solution is correct.

Using row reduction, show that the system of equations x+y+z=1 4x + 2y + z = 1 10x + 4y + z = 1 does not have a unique solution. In fact there is an infinite number of solutions, expressed in terms of a single parameter. Setting z = t, find an expression for x and y in terms of t. Verify (by substitution) that your solution is correct.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.CR: Review Exercises
Problem 54CR: Find if possible values of a,b, and c such that the system of linear equations has a no solution, b...
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Using row reduction, show that the system of equations x+y+z=1 4x + 2y + z = 1 10x + 4y + z = 1 does not have a unique solution. In fact there is an infinite number of solutions, expressed in terms of a single parameter. Setting z = t, find an expression for x and y in terms of t. Verify (by substitution) that your solution is correct.
Transcribed Image Text:Using row reduction, show that the system of equations x+y+z=1 4x + 2y + z = 1 10x + 4y + z = 1 does not have a unique solution. In fact there is an infinite number of solutions, expressed in terms of a single parameter. Setting z = t, find an expression for x and y in terms of t. Verify (by substitution) that your solution is correct.
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