1104 Mrg What's a Determinant -- Sage

#1) 3*x-2*y==4, 5*x+y==13 a=matrix([(4,-2),(13,1)]) b=matrix([(3,4),(6,13)]) c=matrix([(3,-2),(6,1)]) x=det(a)/det(c) y=det(b)/det(c) show(a) show(b) show(c) print('x=',x) print('y=',y)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} 4 & -2 \\ 13 & 1 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} 3 & 4 \\ 6 & 13 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} 3 & -2 \\ 6 & 1 \end{array}\right)$ 
('x=', 2)
('y=', 1)

('x=', 2)
('y=', 1)

#2) 3*x-2*y==4, 5*x+y==13 a=matrix([(3,1,-1),(-3,2,4),(4,-2,-3)]) b=matrix([(2,3,-1),(-1,-3,4),(1,4,-3)]) c=matrix([(2,1,3),(-1,2,-3),(1,-2,4)]) d=matrix([(2,1,-1),(-1,2,4),(1,-2,-3)]) x=det(a)/det(d) y=det(b)/det(d) z=det(c)/det(d) show(a) show(b) show(c) show(d) show('x=') show(x) show('y=') show(y) show('z=') show(z)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 3 & 1 & -1 \\ -3 & 2 & 4 \\ 4 & -2 & -3 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 2 & 3 & -1 \\ -1 & -3 & 4 \\ 1 & 4 & -3 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 2 & 1 & 3 \\ -1 & 2 & -3 \\ 1 & -2 & 4 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} 2 & 1 & -1 \\ -1 & 2 & 4 \\ 1 & -2 & -3 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\verb|x=|$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}3$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\verb|y=|$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-2$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\verb|z=|$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}1$

1104 Mrg What's a Determinant

3174 days ago by MATH4R2013