You will write functions

• B=null basis(A,tol);

• B=range basis(A,tol);

The function null basis takes a matrix A as input, and outputs a basis for the null space of A, obtained via Gaussian elimination (and finding the general solution to Ax = 0). B should be written as columns. The function range basis takes a matrix A as input, and outputs a basis (again written as columns) for the range space of A. For this function, again use Gaussian elimination along with MAALA .

Note for both of these functions, you will need to modify Gaussian elimination for the rectangular case; see pg 43 in MAALA. For both these functions, you will also need to input a tolerence parameter tol so that "s = 0" if |s| < tol in order to decide when a row is to be considered 0.