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Systems of Linear Equations, Row Echelon Form and Number of Solutions

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True or false
1. Every linear system of four equations in five unknowns has infinitely many solutions.

2. If two systems of linear equations have augmented matrices that row reduce to the same reduced row echelon form, then they have the same solution set.

3. If a system of m linear equations in four unknowns has a unique solution, then m must be greater than or equal to four.

4. If a system of m linear equations in four unknowns has no solutions, then m must be greater than or equal to four.

5. A system of three linear equations in three unknowns has a unique solution if and only if its coefficient matrix is row equivalent to the 3x3 identity matrix.

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Solution Summary

Systems of Linear Equations, Row Echelon Form and Number of Solutions are investigated.

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1. False.
It may have no solution. For example, the system ...

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