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);