# Matrix question

• January 23rd 2010, 08:50 AM
Juggalomike
Matrix question
I am not sure exactly, what they are asking me to do, i found a set of numbers that works for this system but its not accepting my answer, which makes me think they are asking for variables? not realy sure

Solve this system:
http://img15.imageshack.us/img15/562/matrixe.png

X1 = | | + | |S
X2 = | | + | |S
X3 = | | + | |S
X4 = | | + | |S
• January 23rd 2010, 11:16 AM
running-gag
Hi

The determinant of the matrix is 0
You can find all variables as functions of only one parameter
• January 25th 2010, 06:59 PM
Juggalomike
Sorry but i dont understand what you mean by that statement, can you clarify?
• January 26th 2010, 05:15 AM
HallsofIvy
The fact that the determinant, $\left|\begin{array}{cccc}1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1\end{array}\right|$ is 0 means the equations are not independent- either there is no solution or there are an infinite number of solutions. If there are an infinite number of solutions, you cannot solve for all 4 variables but rather can solve for three of them in terms of the fourth. For example, from the first equation, $x_2= 3- x_1$ and, from the fourth, $x_4= 12- x_1$. Now, put those into the second or third equation to find $x_3$ the same way. Try both equations to make sure you get the same result so that there is a solution.

Those are the numbers that go into the squares. Letting the parameter, S, be $x_1$, the first row is $x_1= 0+ 1 S$ and the second row would be $x_2= 3- 1 S$. Now, be aware that you could solve for any three of the variables in terms of the fourth and use that as the parameter, S, so there is NOT one single answer. You appear to be using a computer system to input your answer and I have no idea how it will handle the different possible answers. That's one reason I dislike those things.
• January 26th 2010, 07:50 AM
Juggalomike
ah i understand now, thanks alot