Question

**PLEASE USE MATLAB

2. For each system of linear algebraic equations, determine if the system is underdetermined, has an exact solution, or is overdetermined. If the system is underdetermined, find the general solution and then find a particular solution and check your answer. If the system is exact, find the unique solution and check your answer. If the system is overdetermined, find a least squares solution. 3x, + 2x,-4x, + x,-2 -x, +5x2 + 2x, + 3x4 = 4 4x, + x,-35-3 a) x, +2x, -4x,+2 -x, +5x2 + 2x3 + 3x, = 4 4x, + x2-3x3 + 2x4 =-1 b) 3x, +2x2-4x+x,-2 -x, + 5x, + 2x, +3x4 = 4

Answer 1

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Here is the solution using MATLAB.

2 a) Smain.m A-[1-1 1-1:32-41,-1 5 2 3;4 1-30] %Exact solutio n least square solution least-square-a-pinv (A) *B disp ('The augmented matrix is:') rref ([A B])

Code to copy:

a)

%main.m

A = [1 -1 1 -1;3 2 -4 1;-1 5 2 3;4 1 -3 0]

B = [3; 2; 4; 5]

%Exact solution

X = A\B

%least square solution

least_Square=A*pinv(A)*B

disp('The augmented matrix is:')

rref([A B])

b) 8main.m A1-1 1 13 2 -4 1;-1 5 2 3;41 -3 2] %Exact solutio n least square solution least_square-A*pinv (A) *B disp ('The augmented matrix is:') rref (IA B])

1.4186 2.4651 1.0465 -3.0000 least_Square - 3.00000 2.00000 4.00000 -1.00000 The augmented matrix is: ans 1.00000 0.00000 .00000 0.00000 1.41860 0.00000 1.00000 0.00000 0.00000 2.46512 0.00000 0.00000 1.00000 0.00000 1.04651 0.00000 0.00000 0.00000 1.00000 3.00000

Code to copy:

b)

%main.m

A = [1 -1 1 -1;3 2 -4 1;-1 5 2 3;4 1 -3 2]

B = [3; 2; 4; -1]

%Exact solution

X = A\B

%least square solution

least_Square=A*pinv(A)*B

disp('The augmented matrix is:')

rref([A B])

c) Smain.m ΑΞ[1-1 1-1:32-41,-1 5 2 3;4 1-30] %Exact s luti on least square solution least_square-A*pinv (A) *B disp ('The augmented matrix is:') rref (IA B])

2.57644 0.87994 1.61745 -0.35272 least_Square - 3.6667 2.6667 4.0000 6.3333 The augmented matrix is: ans 1.00000 0.00000 .00000 -0.25581 0.00000 0.00000 1.00000 0.00000 0.60465 0.00000 0.00000 0.00000 1.00000 -0.13953 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000

Code to copy:

c)

%main.m

A = [1 -1 1 -1;3 2 -4 1;-1 5 2 3;4 1 -3 0]

B = [3; 2; 4; 7]

%Exact solution

X = A\B

%least square solution

least_Square=A*pinv(A)*B

disp('The augmented matrix is:')

rref([A B])