Can You Spot the Incorrect Answers in These Linear Algebra True/False Questions?

[stryker105]

True or False Questions. I have put my answers to them but one or more is incorrect, can anybody tell me which ones?

Note: The linear system Ax=b of m equations in n unknowns is called:

square if m=n
overdertermined if m>n
undeterdetermined if m<n
homogeneous if b= 0
inhomogeneous b != 0
consistent if it has a solution
inconsistent if it does not have a solution.

Below, we refer to Ax= b of m equations in n unknown simply as "the system". The corresponding homogeneous system is Ax=0

Questions:

1. The general solution of the system equals any particular solution plus the general solution of the corresponding homogeneous system. T

2. An underdetermined system may have no solutions. T

3. An overdetermined system may have a unique solution. T

4. An overdetermined system may have infinitely many solutions. T

5. An underdetermined system may not have a unique solution. F

6. Every homogeneous system is consistent. F

7. An overdetermined system may be consistent. T

8. An underdetermined system may be inconsistent. T

9. The solutions of the system form a linear space if and only if the system is homogeneous. T

10. The null space of A is a subspace of R^n. T

11. The column space of A is a subspace of R^m. T

12. For a square system the column and null spaces of A may be the same. T

13. The system is consistent if and only if b is in the column space of A. T

 

[vela]

It would help if you gave a brief explanation for how you reached each of these answers.

 

[SammyS]

It would help if you gave a brief explanation for how you reached each of these answers.

What vela said is a reflections of the rules for posting in the Homework help section.

This is especially true in your case, since you posted a thread with true/false previously, and never replied to any of the help that was given.

 

[SammyS]

True or False Questions. I have put my answers to them but one or more is incorrect, can anybody tell me which ones?

Note: The linear system Ax=b of m equations in n unknowns is called:

square if m=n
overdertermined if m>n
undeterdetermined if m<n
homogeneous if b= 0
inhomogeneous b != 0
consistent if it has a solution
inconsistent if it does not have a solution.

Below, we refer to Ax= b of m equations in n unknown simply as "the system". The corresponding homogeneous system is Ax=0

Questions:

1. The general solution of the system equals any particular solution plus the general solution of the corresponding homogeneous system. T

2. An underdetermined system may have no solutions. T

3. An overdetermined system may have a unique solution. T

4. An overdetermined system may have infinitely many solutions. T

5. An underdetermined system may not have a unique solution. F

6. Every homogeneous system is consistent. F

7. An overdetermined system may be consistent. T

8. An underdetermined system may be inconsistent. T

9. The solutions of the system form a linear space if and only if the system is homogeneous. T

10. The null space of A is a subspace of R^n. T

11. The column space of A is a subspace of R^m. T

12. For a square system the column and null spaces of A may be the same. T

13. The system is consistent if and only if b is in the column space of A. T

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