| 1. |
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If the graphs of two linear equations are parallel, then there is a unique solution to the system. |
| 2. |
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If the graphs of two linear equations are neither parallel nor the same, then there is a unique solution to the system. |
| 3. |
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If the graphs of two linear equations are not parallel, then there may be no solution to the system. |
| 4. |
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Every system of three linear equations in three unknowns has at least one solution. |
| 5. |
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Some systems of three linear equations in three unknowns have exactly two solutions. |
| 6. |
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Some row reduced matrices have a row of zeros on top. |
| 7. |
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If a matrix has some fractions as entries, then it cannot be row reduced. |
| 8. |
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The system of equations ax + by = 0, cx + dy = 0 has at least one solution, no matter what the values of the coefficients are. |
| 9. |
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If the system of equations ax + by = 0, cx + dy = 0 has a non-zero solution, then it has infinitely many solutions. |
| 10. |
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If the row reduced form of the augmented matrix corresponding to a system of linear equations has a row of zeros, then there are infinitely many solutions. |
| 11. |
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A row reduced matrix always has a 1 in the second column of the second row. |
| 12. |
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Some row reduced matrices have a 2 in the top left-hand corner. |
| 13. |
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The system x + y + z = 1, x = y, y = z, y = 1 is inconsistent. |
| 14. |
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The system x + y + z = 1, x = y, y = 1 + z is inconsistent. |
| 15. |
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If a system of linear equations is inconsistent, then it has infinitely many solutions. |
| 16. |
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If a system of linear equations has infinitely many solutions, then it may be inconsistent. |
| 17. |
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If two of the equations in a system of three linear equations are inconsistent, then the whole system is inconsistent. |
| 18. |
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When we row reduce a matrix, we must always turn each pivot into a 1 before clearing its column, or else errors will result. |
| 19. |
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If the row reduced form of a matrix has more than two non-zero entries in any row, then the corresponding system of equations has infinitely many solutions. |
| 20. |
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If the row reduced form of a matrix has more than two non-zero entries in any row, then the corresponding system of equations either has infinitely many solutions or no solutions. |
