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 (4.2.8) on pg 172 in MAALA
(the definition of basic columns is in the blue box on page 45). 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 param-
eter tol so that “s = 0” if |s| < tol in order to decide when a row is to be
considered 0.