Write a script that will do the following The conditional number of B = [1 2 1.0

Question

Write a script that will do the following The conditional number of B = [1 2 1.00001 1.99999] and inv(B) Conditional number of A = [1 1 1 1 2 -1 1 -1 -2] and inv(A) Solve for the system equation Ax = b defined as: [1 1 1 1 2 -1 1 -1 -2] [x_1 x_2 x_3] = [1 7 3] Show that the system in part 3 is consistent that is the rank(A) = rank[A b]) Solve for the given underdetermined system A_2x = b_2 and show if it is a consistent system [1 1 -1 2 -.5 2.5] [x_1 x_2 x_3] = [1 0] Solve for the given the overdetermined system A_3x = b_3, and show if it is a consistent system [1 2 2 2 1 2] [x_1 x_2] = [3 3 4] Submit the code as (.m) file. Make your work to be presentable.

Explanation / Answer

Matlab code:

%Que1
B = [1, 1.00001;2,1.99999];
Binv = inv(B);
conditiona_number_B = cond(B)
conditiona_number_Binv = cond(Binv)

%Que2
A = [1,1,1; 1,2,-1;1,-1,-2];
Ainv = inv(A);
conditiona_number_A = cond(A)
conditiona_number_Ainv = cond(Ainv)

%Que3
A = [1,1,1; 1,2,-1;1,-1,-2];
B = [1;7;3];
x = linsolve(A,B)

%Que4

rA = rank(A);
rB = rank([A B]);
rA == rB

%Que5
A2 = [1,-1,-0.5; 1,2,2.5];
b2 = [1;0]
x = linsolve(A2,b2)

%consistency
rA = rank(A2);
rB = rank([A2 b2]);
rA == rB

%Que6
A3 = [1,2; 2,1 ; 2,2];
b3 = [3;3;4]
x = linsolve(A3,b3)

%consistency
rA = rank(A3);
rB = rank([A3 b3]);
rA == rB

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