# Need help with Trivial/Non trivial solution

• April 5th 2010, 03:06 PM
supersaiyan
Need help with Trivial/Non trivial solution
http://i43.tinypic.com/s1n3fl.jpg
The questions asks for what value of Z does your set of equations have a non trivial solution?
I am not even sure how to begin.. any hints?
• April 5th 2010, 04:40 PM
Jhevon
Quote:

Originally Posted by supersaiyan
http://i43.tinypic.com/s1n3fl.jpg
The questions asks for what value of Z does your set of equations have a non trivial solution?
I am not even sure how to begin.. any hints?

Hint: create an augmented matrix and solve it using Gauss-Jordan elimination. You will obtain an expression in Z that will allow you to solve for it.
• April 6th 2010, 05:53 AM
HallsofIvy
A homogeneous system of equations will have a non-trivial solution if and only if the determinant of the coefficient matrix is 0.

Solve $\left|\begin{array}{cccc}-2 & 2 & 5 & 4 \\ -3 & 2 & 5 & 7 \\ 6 & -4 & 5 & 0 \\ 1 & 0 & 15 & Z\end{array}\right|= 0$