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Unformatted text preview: MATLAB Project 2 for MAS 3114
Due Friday, October 14
Input the function ﬁle lead.m given below into your MATLAB directory:
while col<=n & row<=m,
1. Apply lead to the following matrices:
(a) A=[1 2 0 4 0 3; 9 18 3 54 0 12; 9 18 0 36 1 20; 3 6 1 18 0 4].
Describe what lead(M) is for an arbitrary matrix M. (Hint: Compare lead(M)
2. Use lead(A) to write a function v=nullrank(A) whose output is a 1 × 2 matrix
v such that v(1,1) is the number of pivot variables in the solution to Ax = 0,
and v(1,2) is the number of free variables in the solution to Ax = 0. Your
ﬁle nullrank.m should not use the MATLAB functions rank or null. Apply
nullrank to the matrices in problem 1 above.
3. Use the MATLAB function rref and the function lead above to write a MATLAB
function N=nullbase(A) which computes a matrix N whose columns form a basis
for the nullspace of A. Your ﬁle nullbase.m should not use the MATLAB functions
rank or null. Compute nullbase(A) and nullbase(A’*A) for the matrices given
in problem 1 above. Make a reasonable conjecture based on these computations.
MATLAB has some methods for constructing matrices which you may ﬁnd useful.
For instance, B=A(:,[1,5,4]) creates a matrix B whose columns are the 1st, 5th, and
4th columns of A. If the second input is a vector with the “logical” data type then
MATLAB interprets it diﬀerently: If A has 6 columns then A(:,[0,1,0,0,1,1]) is a
matrix whose columns are the 2nd, 5th, and 6th columns of A. ...
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- Fall '08