Posted by **Anonymous** on Friday, August 24, 2012 at 11:10am.

If

kx + y + z = 1

x + ky + z = k

x + y + kz = k^2

has unique solution

then k is not equal to 1 and W. What is W?

- Math -
**Steve**, Friday, August 24, 2012 at 11:23am
since the determinant of the system is

| k 1 1 |

| 1 k 1 |

| 1 1 k |

= k^3 - 3k + 2

= (k+2)(k-1)^2

Then k cannot be -1 or 1

- math - oops -
**Steve**, Friday, August 24, 2012 at 11:24am
did I say -1?

I meant -2

- Math -
**drwls**, Friday, August 24, 2012 at 11:26am
The determinant of the three equation left sides cannot be zero.

(k^3 -k) +(1-k) +(1-k) NOT=0

k^3-k NOT= (k-1)

k(k^2 -1) NOT= k-1

k(k+1)NOT =1

k cannot be 0 or -1

W = -1

- Math -
**drwls**, Friday, August 24, 2012 at 11:28am
Steve is right. I left out a 2

## Answer this Question

## Related Questions

- matrices - Let A be a 5 by 4 matris and suppose that the system Ax=b has a ...
- algebra - Which has a Unique solution, No solution, or infinitely many ...
- ENGLISH - 1. Audrey said that Kyle was the most unique person she had even met. ...
- algebra - Consider the following system of inequalities: {(c-1)x^2+2cx+c+4<0...
- maths - Consider the following system of inequalities: {(c−1)x^2+2cx+c+4&#...
- algebra - Consider the following system of inequalities: {(c−1)x^2+2cx+c+4...
- MAths - Consider the following system of inequalities: (c−1)x^2+2cx+c+4&#...
- 7 grade math - Consider two types of nonlinear equations. What unique quality ...
- math - two systems of equations are giving below for each system choosethe best ...
- math,correction - can someone correct this for me. Directions: Solve the ...