Simple questions. I have the following matrix:
I have then 12 equations and 10 variables. I want to only keep independent equations. I can use matlab for this assignment.
Is there a way to do it through matlab? I've been trying to play with equations but unable to prove if the 12 are independant.
On
You can use Gaussian Elimination to attempt to reduce the matrix into Echelon form (Upper Triangular).
Given that you know there are $2$ dependent equations, you should find that as you perform elementary row operations you will find $2$ rows of your $12$x$10$ matrix with zero entries.
This means that the row vectors of our original matrix corresponding to those zero rows are dependent and hence need not be considered when solving the system.
Strictly, what you are demonstrating by doing this is that the Columnspace of our 12 by 10 Matrix is 10 dimensional.
Here's the best explanation I have found for this: https://youtu.be/8o5Cmfpeo6g?t=1077
Use the command Reduced row echelon form in order to identify the pivot rows which correspond to the independent equations.