Gaussian Elimination Solve for variable

[Gurvir]

Homework Statement

Determine the value of k for which the system
x + y + 2z = 3
x + 2y -4z = -3
2 + 8 + kz = -29
has no solutions.

Homework Equations

None

The Attempt at a Solution

Converting to a matrix

1 1 2 3
1 2 -4 -3
2 8 k -29

r2=r2-r1

1 1 2 3
0 1 -6 0
2 8 k -29

r3=r3-2r1

1 1 2 3
0 1 -6 0
0 6 (k-4) -35

r3=r3-6r2

1 1 2 3
0 1 -6 0
0 0 (k+32) -35

So then I figured that:
(k + 32)z = -35
k = (-35/z) - 32

But the problem is I'm doing this online and the solution has to be a real number without variables. So I think I may have gone wrong somewhere. How do I solve for k?

 

[ArcanaNoir]

When you have the row: 0 0 (k+32) -35, what does that row mean? You are right when you say (k+32)z=-35. So, what value of k makes this line untrue? (don't move things around, just look at it like this). It's a particular situation you should be familiar with, as it signals when any row reduced matrix has no solution.

 

[Gurvir]

When you have the row: 0 0 (k+32) -35, what does that row mean? You are right when you say (k+32)z=-35. So, what value of k makes this line untrue? (don't move things around, just look at it like this). It's a particular situation you should be familiar with, as it signals when any row reduced matrix has no solution.

Oh, so (k+32) must equal 0 to make the solution impossible. Which means k = -32?

 

[ArcanaNoir]

You got it :)

 

[Gurvir]

OMG! Ingenious! Thanks guys. Your help is always great!