MATLAB Programming/Advanced Topics/Numerical Manipulation/More complicated matrix operations

Row reduced echelon form
To find the Row reduced echelon form of a matrix just use the MATLAB command rref

Example:

a=[1 2 3; 4 5 6]; b=rref(a);

It's that simple. (I believe that MATLAB uses the Gauss-Jordan elimination method to make this computation; don't quote me on that (I'm not even sure if there are other methods)).

Inverse
To find the inverse of a matrix use the MATLAB command inv. (note that the matrix must be square)

Example:

a=[1 2 3;4 5 6;7 8 9]; b=inv(a);

The Jacobian
t=jacobian(e,w);

e is a scalar vector, w is a vector of functions. Also, this does not solve equations symbolically unless you define the w vector functions as symbolics prior to executing this statement.

Example: syms x y z; w=[x y z]; e=[1 2 3]; t=jacobian(e,w);