Question

using matlab Write your own routine for Gaussian elimination without any pivoting. Input for the routine should consist of the number (n) of equations and the augmented matrix. Output should be the vector solution of the system. Test your code by using it to solve the following two problems: a) x + y + w + z = 10, 2x + 3y + w + 5z = 31, −x + y − 5w + 3z = −2, 3x + y + 7w − 2z = 18

Answer #1

**MATLAB
Code:**

close all

clear

clc

% x + y + w + z = 10

% 2x + 3y + w + 5z = 31

% −x + y − 5w + 3z = −2

% 3x + y + 7w − 2z = 18

A = [ 1 1 1 1;

2 3 1 5;

-1 1 -5 3;

3 1 7 -2];

b = [10 31 -2 18]';

Ag = [A b];

n = size(A, 1);

x = gauss_elim(n, Ag)

function x = gauss_elim(n, Ag)

A = Ag(:,1:end-1);

b = Ag(:,end);

nb = length(b);

x = zeros(1,n);

% Gaussian elimination

for i = 1:n-1

if A(i,i) == 0

t = min(find(A(i+1:n,i) ~= 0) + i);

if isempty(t)

disp ('Error: A matrix is singular');

return

end

temp = A(i,:); tb = b(i);

A(i,:) = A(t,:); b(i) = b(t);

A(t,:) = temp; b(t) = tb;

end

for j = i+1:n

m = -A(j,i) / A(i,i);

A(j,i) = 0;

A(j,i+1:n) = A(j,i+1:n) + m*A(i,i+1:n);

b(j) = b(j) + m*b(i);

end

end

% Back substitution

x(n) = b(n) / A(n,n);

for i = n-1:-1:1

x(i) = (b(i) - sum(x(i+1:n) .* A(i,i+1:n))) / A(i,i);

end

end

**Output:**

x =

1 2 3 4

Solve the following system of equations using Gaussian
elimination. Write the anwser as ordered triples and please show
steps.
2x+y+2z=18
x-y+2z=9
x+2y-z=6

Use Gaussian elimination to find the complete solution to the
following system of equations, or show that none exists.
{5x + 17y + 7z = 14
{2x + 7y -5z = -3
{ x + 3y - 3z = 8
Find the row-echelon form of the matrix for the given system of
equations. (Do not include the vertical bar in the
augmentedmatrix.)
Select the correct choice below and, if necessary, fill in the
answer boxes to complete your choice.
A....

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination.If the system has an
infinite number of solutions, express x, y, and
z in terms of the parameter t.)
3x + 3y + 9z = 6
x + y + 3z = 2
2x + 5y + 15z = 10
-x + 2y + 6z = 4
(x, y, z)
= ?

Solve system of equations using matrices. Make a 4x4 matrix and
get the diagonal to be ones and the rest of the numbers to be
zeros
2x -3y + z + w = - 4
-x + y + 2z + w = 3
y -3z + 2w = - 5
2x + 2y -z -w = - 4

1)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express your answer in terms
of the parameters t and/or s.)
x1
+
2x2
+
8x3
=
6
x1
+
x2
+
4x3
=
3
(x1,
x2, x3)
=
2)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express...

4. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions. In the latter case, present
the solutions in parametric form.
3x + 6y + 3z = -6
-2x -3y -z = 1
x +2y + z = -2

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