Create a script for the following exercises Let A 2 7 3 9 3

Create a script for the following exercises: Let A = [2 -7 -3 -9 3 7 4 3 5 0 1 -6 -5 0 3 -4], b = [8 7 5 -3]. Is b in the range of the transformation T: x rightarrow Ax? If so, print on screen an x whose image under transformation T is b. Consider transformation: T(x) = T ([x_1 x_2 x_3 x_4]) = [x_1 - x_3 + x_4 4x_2 3x_4 - 2x_1 x_3/2 2x_2 + 5x_4] Print on screen the standard matrix of T.

Solution

1. MATLAB script for the problem is as below:

clear all;
close all;
A=[2 3 5 -5; -7 7 0 0; -3 4 1 3; -9 3 -6 -4];
b=[8; 7; 5; 3];
augA=[A b];
R = rref(augA);
if rank(A)<rank(R)
disp(\'inconsistent, so b is not in the range T\');
elseif rank(A)==4
disp(\'unique solution, b is in the range T\');
else
disp(\'infinitely many solution, b is in the range T\');
end

Output of the script is:

inconsistent, so b is not in the range T