disp('Homework sSet no.1')
disp('Section 1.1')
pause
disp('Problem 2')
A2=[1 -3 7;2 6 8]
pause
xx=[-2 7];
y1=xx/3-7/3;
y2=-xx/3+4/3;
plot(xx,y1,'y-',xx,y2,'r-')
rref(A2)
pause
disp('Problem 18')
A18=[2 3 4 3;3 6 -2 1;5 -9 6 1]
rref(A18)
pause
disp('Problem 24')
A24=[2 -1 1 -1 3;3 -2 4 -1 4;5 2 -3 -4 0;-1 -1 3 4 2]
rref(A24)
pause
disp('Problem 33')
disp('Compare also the in-class exercises for small steps')
xx=[0,1,2,-1]
yy=[1,2,3,6]
hold off
a=polyfit(xx,yy,3)
xxx=[-1.5:0.25:2.5];
yyy=polyval(a,xxx);
plot(xx,yy,'r*',xxx,yyy,'c-')
disp('Result displayed in PLOT window - don''t miss it!')
pause
disp('Problem 50')
pause
disp('First change variables u=1/(x-y) and v=1/(x+y)')
disp('Then the (u,v) solution is:')
pause
A50=[2 1 3;5 6 4]
step1=rref(A50)
u=step1(1,3)
v=step1(2,3)
pasue
disp('Then solve a new system for x and y')
pause
A50a=[u -u 1;v v 1]
rref(A50a)
pause
disp('Section 1.2')
pause
disp('Problem 2')
pause
A2=[1 2 -1;0 1 -1;0 0 0]
rref(A2)
disp('unique solution')
pause
disp('Problem 8')
pause
A8=[1 4 0 -2;0 0 1 3;0 0 0 1]
disp('inconsistent, no solution')
pause
disp('Problem 10')
A10=[1 2 0 1 -3;0 0 1 2 4]
disp('consistent: 2-parameter family of solutions:')
disp('x=(-3-t-2s,s,4-2t,t)')
pause
disp('Problem 14')
pause
A14=[1 1 1 0;1 -1 1 0;1 1 -1 0]
rref(A14)
pause
disp('Problem 20')
pause
A20=[1 -7 17;2 3 0;3 -4 17]
rref(A20)
pause
disp('Problem 28')
pause
disp('MATLAB is not suitable here - better try MAPLE, best use paper!')