# Thread: for which values of k the system has infinite number of solutions ?

1. ## for which values of k the system has infinite number of solutions ?

Hello,

I have a small question, I am not sure about it.

I had a system of linear equations. I was asked for which values of k, the system has infinite number of solutions, with 2 degrees of freedom.

The degrees of freedom thing kind of confused me, usually I know how to approach these things.

I have eliminated the system, the attached photo contains the matrix of the system (including the vector B as last column) after I eliminated it in the Gausian way.

What do I do now ? What's with the degrees of freedom ?

if I didn't have the degrees of freedom condition I would say k=2....does it change the answer ?

2. ## Re: for which values of k the system has infinite number of solutions ?

Degrees of freedom? Is this statistics?

If k = 2, like you said, we have a row of all 0.

What does that tell you?

Spoiler:

It should say you have a free variable.