"Show that the following system of equations is not consistent for any k ∈ ℝ:

a-2b-4c=-1
-2a-4c=k(k-2)
2a-b+c=1"

The full answer is not necessarily needed, but could someone point me towards the right direction as I have absolutely no idea where to start right now. Thanks.

Question

"Show that the following system of equations is not consistent for any k ∈ ℝ:

a-2b-4c=-1
-2a-4c=k(k-2)
2a-b+c=1"

The full answer is not necessarily needed, but could someone point me towards the right direction as I have absolutely no idea where to start right now. Thanks.

fifciol · Answer

take first and third equation and eliminate b. Determine a or c and substitute in second equation. You will get the equation with one variable k. It's a quadratic equation. Check out if there is any solutions for k( determine delta, should be less than zero)

anonymous · Answer

Thanks a bunch, the determinant was -4 which obviously means no real solutions :)

fifciol · Answer

yes I found the same:)