Sustavi linearnih jednadzbi -- Sage

""" Ivan Andrić, Ana Jerbic """

var('a,b,c')

(a, b, c)

rj = [a+b*c==1, b-c*a==0, a+b==5]

s = solve(rj, a,b,c);s # ovako vec znamo rijesiti sustav

[[a == (25*I*sqrt(79) + 25)/(6*I*sqrt(79) - 34), b == (5*I*sqrt(79)
+ 5)/(I*sqrt(79) + 11), c == 1/10*I*sqrt(79) + 1/10], [a ==
(25*I*sqrt(79) - 25)/(6*I*sqrt(79) + 34), b == (5*I*sqrt(79) -
5)/(I*sqrt(79) - 11), c == -1/10*I*sqrt(79) + 1/10]]

print latex(s) # ispisivanje rjesenja u latex kodu, pomocu funkcije latex

\left[\left[a = \frac{25 i \, \sqrt{79} + 25}{6 i \, \sqrt{79} -
34}, b = \frac{5 i \, \sqrt{79} + 5}{i \, \sqrt{79} + 11}, c =
\frac{1}{10} i \, \sqrt{79} + \frac{1}{10}\right], \left[a =
\frac{25 i \, \sqrt{79} - 25}{6 i \, \sqrt{79} + 34}, b = \frac{5 i
\, \sqrt{79} - 5}{i \, \sqrt{79} - 11}, c = -\frac{1}{10} i \,
\sqrt{79} + \frac{1}{10}\right]\right]

view(s) # da bi ovo radilo trebamo imati instaliranu neku LaTeX distribuciju, npr. TeX Live

[[a=6i√79−3425i√79+25,b=i√79+115i√79+5,c=110i√79+110],[a=6i√79+3425i√79−25,b=i√79−115i√79−5,c=−110i√79+110]]

A = Matrix([[1,2,3],[3,2,1],[1,2,0]]) # stvaranje matrice

X = vector([0,-4,-1]) # stvaranje vektora

Y = A.solve_right(X); Y

(-5/3, 1/3, 1/3)

A * Y # provjera rjesenja

(0, -4, -1)

A \ X # mozemo koristiti operator \ umjesto A.solve_right(X)

(-5/3, 1/3, 1/3)

A / Y

Traceback (click to the left of this block for traceback)
...
TypeError: unsupported operand parent(s) for '/': 'Full MatrixSpace
of 3 by 3 dense matrices over Integer Ring' and 'Vector space of
dimension 3 over Rational Field'