True/False Quiz for Chapter 2

Systems of Linear Equations and Matrtices

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1. If the graphs of two linear equations are parallel, then there is a unique solution to the system. True False

2. If the graphs of two linear equations are neither parallel nor the same, then there is a unique solution to the system. True False

3. If the graphs of two linear equations are not parallel, then there may not be a solution to the system. True False

4. Every system of three linear equations in three unknowns has at least one solution. True False

5. Some systems of three linear equations in three unknowns have exactly two solutions. True False

6. Some row reduced matrices have a row of zeros on top. True False

7. If a matrix has some fractions as entries, then it cannot be row reduced. True False

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. True False

9. If the system of equations ax + by = 0, cx + dy = 0 has a non-zero solution, then it has infinitely many solutions. True False

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. True False

11. A row reduced matrix always has a 1 in the second column of the second row. True False

12. Some row reduced matrices have a 2 in the top left-hand corner. True False

13.The system x + y + z = 1, x = y, y = z, y = 1 is inconsistent. True False

14. The system x + y + z = 1, x = y, y = 1 + z is inconsistent. True False

15. If a system of linear equations is inconsistent, then it has infinitely many solutions. True False

16. If a system of linear equations has infinitely many solutions, then it may be inconsistent. True False

17. If two of the equations in a system of three linear equations are inconsistent, then the whole system is inconsistent. True False

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. True False

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. True False

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. True False