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Linear systems and echelon matrices

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The echelon form can be used to determine if a linear system is consistent.
Example of using the echelon form to determine if a linear system is consistent.
The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.
The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.

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The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.

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The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.Close match
A consistent system with more variables than equations has infinitely many solutions.Close match
All echelon forms of a linear system have the same free variablesClose match
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The number of solutions to a linear systemClose match
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Equivalence theorem for nonsingular matrices: there is a pivot position in every row of A.Close match
The echelon form can be used to determine if a linear system is consistent.Close match
A real or complex linear system has zero, one, or infinitely many solutionsClose match
The matrix equation Ax=b has a solution if and only if b is a linear combination of the columns of A.Close match
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The rank of a matrix equals number of pivots in a reduced row echelon form.Close match
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Definition of echelon form of a linear systemClose match
Definition of free/independent variable in a linear systemClose match
Equivalence theorem for nonsingular matrices: the equation Ax=b has a unique solution for all b.Close match
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