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Linear systems and matrices

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Matrix equations
Linear systems and echelon matrices
A linear system is equivalent to a matrix equation.
A linear system is equivalent to a vector equation.
Terminology
Using matrices to solve linear systems
Row-equivalent augmented matrices represent equivalent systems

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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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Linear systems and echelon matrices

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Definition of echelon form of a linear systemClose match
Echelon matricesClose match
All echelon forms of a linear system have the same free variablesClose match
Definition of (row) echelon form of a matrixClose match
TerminologyClose match
Linear systems and matricesClose match
Definition of matrix in reduced row echelon formClose match
Example of putting a matrix in echelon form and identifying the pivot columnsClose match
The echelon form can be used to determine if a linear system is consistent.Close match
Every matrix is row-equivalent to a matrix in reduced row echelon form.Close match
Definition of reduced row echelon form of a matrixClose match
Every matrix is row-equivalent to only one matrix in reduced row echelon form.Close match
Definition of (echelon matrix/matrix in (row) echelon form)Close match
Example of putting a matrix in echelon formClose match
Using matrices to solve linear systemsClose match
Example of using the echelon form to determine if a linear system is consistent.Close match
Example of (echelon matrix/matrix in (row) echelon form)Close match
The nonzero rows of an echelon form of a matrix are linearly independent.Close match
The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.Close match
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

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