Question

On Matlab: Use both X=A\b and X=inv(A)∗b to find x,y,z. Use tic toc to time each method.

Then create a general solver to solve any linear system of n equations and n unknowns of the form AX = b. Allow the user to input the n×n matrix A and n×1 column vector b. Use X = A\b to solve the system in your script and display the solution to the user. Try your solver with A = randi(50, 10),

b = randi(20, 10, 1) and A = randi(3, 500), b = randi(7, 500, 1).

Solve the system of equations: z -2y 232 52 Define A as the matrix of coefficients, X y, zl and b is a column vector representing the right- hand side of these equations. 3 7 -61 4 1 2 23 Recall the matrix form of this equation is AX b with solution X A 1b 3 7 -6 1 -2 23 -3 La L-6 0 5

Answer 1

ex.m

function x=y(A,B)
% Get the size of the matrix A and B
[m,n] = size(A);
[i,j] = size(B);

% Check if the dimension matches
if(n ~= i)
fprintf('Matrix dimension does not match\n');
else
% Start the tic.
tic;
fprintf('Using A\\B \n');
x = A\B
fprintf('Using inv(A)*B\n');
x = inv(A)*B
timeToComplete = toc
end
end

OUTPUT:

>> A = [3 7 6;1 -2 23;-6 0 5];
>> B = [4; -3; 2 ];
>> ex(A,B)

Using A\B

x =

-0.3726
0.7715
-0.0471

Using inv(A)*B

x =

-0.3726
0.7715
-0.0471

timeToComplete =

4.1055e-004

ans =

-0.3726
0.7715
-0.0471