Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations
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System of linear equations
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If a homogeneous system of linear equations has a nontrivial solution, then the system has infinitely many solutions.
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Way to go! The possibility of the number of solutions of any system of linear equations are zero, one, or infinity.
Since a homogeneous system has the zero solution, if it has nontrivial solutions, it has two solutions. Hence there should be infinitely many solutions.Incorrect
Review the following fact: the possibility of the number of solutions of any system of linear equations are zero, one, or infinity.
Since a homogeneous system has the zero solution, if it has nontrivial solutions, it has two solutions. Hence there should be infinitely many solutions.
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