- #1

CynicusRex

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Member warned about posting with no template, and with incomplete problem statement

## Homework Statement

The assignment is to find all values of k (in R) for which the system has 0 solutions, 1 solution and infinite solutions. If there are infinite solutions, find the amount of free variables.

The system of linear equations:

kx + (k+1)y + z = 0

kx + y + (k+1)z = 0

2kx + y + z = k+1

## Homework Equations

Now k=-1

## The Attempt at a Solution

So I was correct that this system is undefined when k=0.

Then I thought this system had infinite solution when k =/= 0. But here I'm wrong.

Apparently if k=-1 then there are infinite solution with one free variable. However, when I plug in -1 then all solutions are -1/2.

I don't understand why this is infinite.

I did my row operations as practise.

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