clear
% the backslash command


A=[3 1 4 6; 3 5 6 2; 8 9 0 54; 3 5 734 2];
bq=[3; 5; 6; 7];

xq=A\bq;   %type format rat to get this in fractional form

% sometimes it goes wrong

G=[0 0; 0 0];
g=[1;2];

y=G\g;

% check out xlsread for reading data etc. from excel files

% checking sdd with a function
R=[4 -1 1; 4 -8 1; -2 1 5];
verify=checksdd(R)

if verify==1
    ee=3
else
    ee=0
end

% solvin Ax=b with LU factorization

Q=[3 4 5; 6 7 2; 3 1 6];
m=length(Q);
b(1:m,1)=[3; 4; 5];
b(1:m,2)=[1; 2 ; 3];
b(1:m,3)=[4; 5; 6];

[L, U, P]=lu(Q);

tic %turn on stopwatch
for i=1:3
    if P==eye(m)
        x(1:m,i)=U\(L\b(:,i));
    else
        x(1:m,i)=U\(L\(P*b(:,i)));
    end
end

t1=toc  %turn off stopwatch

tic

for i=1:3
    x2(1:m,i)=Q\b(:,i);
end

t2=toc