True/False Quizzes for
Finite Mathematics
Topic: Systems of Linear Equations
and Matrices
(Chapter 2)

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1. If the graphs of two linear equations are parallel, then there is a unique solution to the system.
2. If the graphs of two linear equations are neither parallel nor the same, then there is a unique solution to the system.
3. If the graphs of two linear equations are not parallel, then there may be no solution to the system.
4. Every system of three linear equations in three unknowns has at least one solution.
5. Some systems of three linear equations in three unknowns have exactly two solutions.
6. Some row reduced matrices have a row of zeros on top.
7. If a matrix has some fractions as entries, then it cannot be row reduced.
8. 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. If the system of equations ax + by = 0, cx + dy = 0 has a non-zero solution, then it has infinitely many solutions.
10. 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. A row reduced matrix always has a 1 in the second column of the second row.
12. Some row reduced matrices have a 2 in the top left-hand corner.
13. The system x + y + z = 1, x = y, y = z, y = 1 is inconsistent.
14. The system x + y + z = 1, x = y, y = 1 + z is inconsistent.
15. If a system of linear equations is inconsistent, then it has infinitely many solutions.
16. If a system of linear equations has infinitely many solutions, then it may be inconsistent.
17. If two of the equations in a system of three linear equations are inconsistent, then the whole system is inconsistent.
18. 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. 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. 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.

Last Updated: July, 2000
Copyright © 2000 Stefan Waner & Steven R. Costenoble