# Thread: use cramer's rule to determine what values of (variable) yield.....

1. ## use cramer's rule to determine what values of (variable) yield.....

Ok well.......

the system:

x- y+ 3z= -8
2x+ 3y- z= 5
3x+ 2y+ 2kz= -3k

So using cramer's rule i first had to find the determinants.

They are as follows:

D=10k-10
Dx= -14k-14
Dy= 21k-21
Dz= -15k+15

Ok, well those are the determinants.

Now i am supposed to use Cramer's Rule to determine what value(s) oh k yield............

a)no solution?
b)exactly on solution?
c)infinitely many solutions?

I thank you all in advanced

2. Originally Posted by Danktoker
Ok well.......

the system:

x- y+ 3z= -8
2x+ 3y- z= 5
3x+ 2y+ 2kz= -3k

So using cramer's rule i first had to find the determinants.

They are as follows:

D=10k-10
Dx= -14k-14
Dy= 21k-21
Dz= -15k+15

Ok, well those are the determinants.

Now i am supposed to use Cramer's Rule to determine what value(s) oh k yield............

a)no solution?
b)exactly on solution?
c)infinitely many solutions?

I thank you all in advanced

If $\displaystyle \Delta\neq 0\iff k\neq 1$ then there's a unique solution, given (this is Cramer's Rule) by $\displaystyle \begin{pmatrix}\frac{\Delta_x}{\Delta}\\{}\\\frac{ \Delta_y}{\Delta}\\{}\\\frac{\Delta_z}{\Delta}\end {pmatrix}$ .

If $\displaystyle k=1$ then bringing the augmented matrix into echelon form we get that there are infinite solutions.

Tonio

3. Hi Tonio Thank you very much for the reply.

Just curious about how those deltas work, we have never talked about them.