Does the augmented matrix corresponds to a consistent linear system?

[frctl]

Find all values of k for which the given augmented matrix corresponds to a consistent linear system.



How should I proceed..

 

[Otis]

Does the augmented matrix corresponds to a consistent linear system?

Hello frctl. Use row operations, to get row echelon form. If the bottom row contains all zeros except for the rightmost element, then the system is inconsistent; otherwise, it's consistent.

Find all values of k for which the given augmented matrix corresponds to a consistent linear system.

Continue to reduced row echelon form, and you'll have expressions for the system's solution in terms of k. Those two expressions ought to make clear which values of k lead to Real numbers.

?

 

[frctl]

Find all values of k for which the given augmented matrix corresponds to a consistent linear system.

 

[Dr.Peterson]

This is a repeat post. Does that imply that the other answer was not suitable?

Perhaps you need to show us what methods you know for answering it.

One elementary way is to translate it into a system:

x + ky = -4​

4x + 8y = 2​

What would it take for this to be inconsistent? What would you do to find out?

For example, is this system consistent? (k=1)

x + y = -4​

4x + 8y = 2​

How about this one? (k=2)

x + 2y = -4​

4x + 8y = 2​

 

[frctl]

I'm not sure, I haven't learned to use row operations to get row echelon form.

Could you help me with doing this step by step?

 

[Dr.Peterson]

It's very helpful to know that you don't know row operations. So, what do you know that you can use? What are you able to do with an augmented matrix?

Please demonstrate how you would check whether my example systems are consistent (with or without using a matrix); that will help us know what to suggest to you.

 

[mmm4444bot]

… I haven't learned to use row operations …

Have you seen the forum guidelines' summary (partially quoted below)? From where does this exercise come? Are you in a math class?

1. From where does your question come?

It really helps to know why you're working on math or what math course you're taking. There are many ways to find the same answers. We'd like to discuss the method that you're learning and to explain at your level of study.

 

[Otis]

Are you finished with this exercise?

?

 

[frctl]

Yes, thank you.

 

[Otis]

Good. What method did you decide on? Can you share your answer?

?