# Thread: Practical Applications of Matrices

1. ## Practical Applications of Matrices

I'm looking to understand practical applications of matrices, involving flow of water. One such question is this:

The attached figure shows known flow rates of hydro carbons into and out of a network of pipes at an oil refinery.
a) Set up a linear system whose solution provides the unknown flow rates.
b) Solve the system for the unknown flow rates.
c) Find the flow rates and directions of flow if x4=50 and X6=0.

I have attached a crudely drawn representation of the figure I am supposed to use. I know how to figure out missing values for a two dimensional figure, but I'm unsure of how to do a three dimensional one...

2. Originally Posted by Hellreaver
I'm looking to understand practical applications of matrices, involving flow of water. One such question is this:

The attached figure shows known flow rates of hydro carbons into and out of a network of pipes at an oil refinery.
a) Set up a linear system whose solution provides the unknown flow rates.
b) Solve the system for the unknown flow rates.
c) Find the flow rates and directions of flow if x4=50 and X6=0.

I have attached a crudely drawn representation of the figure I am supposed to use. I know how to figure out missing values for a two dimensional figure, but I'm unsure of how to do a three dimensional one...
the linear system you're looking for is this:

$\displaystyle x_1-x_2=-25$

$\displaystyle x_1+x_3=200$

$\displaystyle x_3-x_4-x_5=-150$

$\displaystyle x_2+x_4-x_6=175$

$\displaystyle x_5+x_6=200.$

now solve the equation by reducing the following matrix to echelon form:

$\displaystyle \begin{bmatrix}1 & -1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & -1 & 0 \\ 0 & 1 & 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 1 & 1 \end{bmatrix}$

3. Why is the last column of the matrix 0s and 1s? Shouldn't it be the constants in the linear system?

4. Originally Posted by Hellreaver
Why is the last column of the matrix 0s and 1s? Shouldn't it be the constants in the linear system?
sure, i forgot! so $\displaystyle \begin{bmatrix}-25 \\ 200 \\ -150 \\ 175 \\ 200 \end{bmatrix}$ is the seventh column of the matrix.