# Not solvable system of linear equations in Mathematica

• November 5th 2010, 09:44 AM
Nforce
Not solvable system of linear equations in Mathematica
How can I find $t$ for system of linear equations, that the system would not be solvable?

I tryed with this code:

Code:

x = 10 y = 10 z = 10 Solve[{ 9 x - 8 y + t*z == 1, 6 x - 8 y - 5 z == 1,  3 x  -7 y + 9 z == 1}, {t}]
• November 5th 2010, 09:50 AM
Ackbeet
You have a highly over-determined system there. There are no solutions. Think about it:

90-80+10t=1
60-80-50=1
30-70+90=1

Some of those equations are downright incorrect. I would review your steps for arriving at that system of equations. What's the bigger context for this problem?
• November 5th 2010, 09:59 AM
Nforce
Sorry, forget x,y,z values.

I need to find t to be not solvable. For t = 1, it's solvable, for t = 2 it's solvable and so on...
but when it's not?
• November 5th 2010, 10:01 AM
Ackbeet
Ok. Try setting

$\left|\begin{matrix}9&-8&t\\6&-8&-5\\3&-7&9\end{matrix}\right|=0.$

That's a determinant there. What do you get?
• November 5th 2010, 10:03 AM
Ackbeet
Whoops. That approach won't work. Take a look at this thread. Make sure you scroll all the way down to the end to get the real reason why that works.
• November 5th 2010, 10:13 AM
Nforce
I get a solution. Great.