Question

Problem 5: For the following matrices, use MATLAB to find the rank and the Row Reduced Echelon Form (RREF) of each of the following matrices. Verify your answers by solving the question by hand. 0-1 1 -2 b) B c) C-2 2 -2 0 -1 3 3 2

Thanx in advance.

Answer 1

0-00 2 3 3 At

3 2 1 32 2. 3 3 13 3 2 2. 2 3

3 1 2 R- R lLR 2 1 O I 2 012 Ru -> R

Code

format rat
A=[-1 1;-1 0;0 -1;-1 -2]
disp('rref(A)')
disp(rref(A))
disp('rank(A)')
disp(rank(A))
B=[1 3 2 1;2 -3 0 -2]
disp('rref(B)')
disp(rref(B))
disp('rank(B)')
disp(rank(B))
C=[2 -3 -2 3;-2 2 -2 0;-1 3 3 2;-3 -2 -2 2]
disp('rref(C)')
disp(rref(C))
disp('rank(C)')
disp(rank(C))

Output

Commands rref (A) rank(A) Calumns 1 through 2 Columns 3 through 4 rref(B) Columns 1 through 2 Calumns 3 through 4 2/3 4/9 4/9 rank (B) Columns 1 through 2 Calumns 3 through 4 2 rref (c) Columns 1 through 2 Columns 3 through 4 rank(C)