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O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. SSx - 7y = 0 O False, consider the following system: 3x +y = 0. f6x + 2y = 0 4x + y = 0. O False, consider the following system: (b) A system of linear equations with fewer equations than variables always has at least one solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. O False, consider the following system: *+y-z7 -7x-7y + 7z = -49. O False, consider the following system: -7x - 7y + 72 - -1.

O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. SSx - 7y = 0 O False, consider the following system: 3x +y = 0. f6x + 2y = 0 4x + y = 0. O False, consider the following system: (b) A system of linear equations with fewer equations than variables always has at least one solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. O False, consider the following system: *+y-z7 -7x-7y + 7z = -49. O False, consider the following system: -7x - 7y + 72 - -1.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 3CE
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Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) A homogeneous system of linear equations must have at least solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. O False, consider the following system:5x - 7y = 0 3x + y = 0. 6x + 2y = 0 O False, consider the following system: 4x + y = 0. (b) A system of linear equations with fewer equations than variables always has at least one solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. x + y - z = 7 O False, consider the following system: 1-7x - 7y + 72= -49. x + y - z = 7 -7x - 7y + 7z -1. O False, consider the following system:
Transcribed Image Text:Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) A homogeneous system of linear equations must have at least solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. O False, consider the following system:5x - 7y = 0 3x + y = 0. 6x + 2y = 0 O False, consider the following system: 4x + y = 0. (b) A system of linear equations with fewer equations than variables always has at least one solution. O True, there is always the trivial solution, when all variables are equal to 1. O True, there is always the trivial solution, when all variables are equal to 0. O True, there is always the trivial solution, when all variables are written in terms of t. x + y - z = 7 O False, consider the following system: 1-7x - 7y + 72= -49. x + y - z = 7 -7x - 7y + 7z -1. O False, consider the following system:
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