Inconsistent Linear Systems: Solving for k

[Math100]

Homework Statement

For what value(s) of k is the linear system with augmented matrix inconsistent?

Homework Equations

None.

The Attempt at a Solution

I know that inconsistent means no solution. So do I set k=2k and solve for k?

 

[NFuller]

The most direct way to declare that a system is inconsistent is by looking for the value of $k$ which causes the determinant of the matrix to be zero. Since this is a fairly simple system however, you could easily pick a value of $k$ which causes one of the rows to be a multiple of the other.

 

[Mark44]

Homework Statement

For what value(s) of k is the linear system with augmented matrix inconsistent?

Homework Equations

None.

The Attempt at a Solution

I know that inconsistent means no solution. So do I set k=2k and solve for k?View attachment 219506

No.
What is the system of equations that your augmented matrix represents?

Also, what does the thing that looks like a backwards S?

Edit: Your attempt at a solution is just barely enough to get by. Other mentors would not have been as generous. In future posts, please make more of an attempt at solving the problems you're asking about.

 

[Math100]

k+2=1
1+2k=1

 

[Mark44]

k+2=1
1+2k=1

So what value of k would make it so that this system of equations doesn't have a solution? One suggestion has already been given.

Going in another direction, these equations represent lines in the plane. Do these planes intersect, which would give one or possibly an infinite number of solutions, or do they not intersect at all?

 

[Ray Vickson]

k+2=1
1+2k=1

These are the world's easiest equations to deal with. Why are you having trouble?

 

[ehild]

k+2=1
1+2k=1

The augmented matrix in the OP represents the system of equation
kx+2y=1
x+2ky=1

 

[ehild]

The most direct way to declare that a system is inconsistent is by looking for the value of $k$ which causes the determinant of the matrix to be zero. Since this is a fairly simple system however, you could easily pick a value of $k$ which causes one of the rows to be a multiple of the other.

Zero determinant does not necessarily imply that the system is inconsistent.

 

[Math100]

Got it!

 

[Mark44]

Got it!

What did you get for k?

 

[Math100]

-1

 

[Math100]

How to give award to best answer?

 

[Math100]

Zero determinant does not necessarily imply that the system is inconsistent.

Thank you so much!

 

[ehild]

You are welcome