MathAction SandBoxCS224

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axiom

[1/2, 3/4, 2/3]

$\label{eq1}\left[{1 \over 2}, \:{3 \over 4}, \:{2 \over 3}\right]$

(1)

Type: List(Fraction(Integer))

axiom

matA := matrix [[0,0,80],[250,0,-40],[250,-250,80]]

$\label{eq2}\left[ \begin{array}{ccc} 0 & 0 &{80} \ {250}& 0 & -{40} \ {250}& -{250}&{80}$

(2)

Type: Matrix(Integer)

axiom

invmatA := inverse matA

$\label{eq3}\left[ \begin{array}{ccc} {1 \over{500}}&{1 \over{250}}& 0 \ {3 \over{500}}&{1 \over{250}}& -{1 \over{250}} \ {1 \over{80}}& 0 & 0$

(3)

Type: Union(Matrix(Fraction(Integer)),...)

axiom

vecA := [300,300,0]

$\label{eq4}\left[{300}, \:{300}, \: 0 \right]$

(4)

Type: List(NonNegativeInteger)

axiom

invmatA * vecA

$\label{eq5}\left[{9 \over 5}, \: 3, \:{{15}\over 4}\right]$

(5)

Type: Vector(Fraction(Integer))

axiom

matB := matrix [[0,0,l * 72],[250,0,l * -36],[250,-250,l * 72]]

$\label{eq6}\left[ \begin{array}{ccc} 0 & 0 &{{72}\ l} \ {250}& 0 & -{{36}\ l} \ {250}& -{250}&{{72}\ l}$

(6)

Type: Matrix(Polynomial(Integer))

axiom

invmatB := inverse matB

$\label{eq7}\left[ \begin{array}{ccc} {1 \over{500}}&{1 \over{250}}& 0 \ {3 \over{500}}&{1 \over{250}}& -{1 \over{250}} \ {1 \over{{72}\ l}}& 0 & 0$

(7)

Type: Union(Matrix(Fraction(Polynomial(Integer))),...)

axiom

vecB := [300,300,0]

$\label{eq8}\left[{300}, \:{300}, \: 0 \right]$

(8)

Type: List(NonNegativeInteger)

axiom

invmatB * vecB

$\label{eq9}\left[{9 \over 5}, \: 3, \:{{25}\over{6 \ l}}\right]$

(9)

Type: Vector(Fraction(Polynomial(Integer)))

axiom

matC := matrix [[l1 * 0,l1 * 0,l1 * 80],[l2 * 250,l2 * 0,l2 *
-40],[l3 * 250,l3 * -250,l3 *80]]

$\label{eq10}\left[ \begin{array}{ccc} 0 & 0 &{{80}\ l 1} \ {{250}\ l 2}& 0 & -{{40}\ l 2} \ {{250}\ l 3}& -{{250}\ l 3}&{{80}\ l 3}$

(10)

Type: Matrix(Polynomial(Integer))

axiom

invmatC := inverse matC

$\label{eq11}\left[ \begin{array}{ccc} {1 \over{{500}\ l 1}}&{1 \over{{250}\ l 2}}& 0 \ {3 \over{{500}\ l 1}}&{1 \over{{250}\ l 2}}& -{1 \over{{250}\ l 3}} \ {1 \over{{80}\ l 1}}& 0 & 0$

(11)

Type: Union(Matrix(Fraction(Polynomial(Integer))),...)

axiom

vecC := [l1 * 300,l2 * 300,0]

$\label{eq12}\left[{{300}\ l 1}, \:{{300}\ l 2}, \: 0 \right]$

(12)

Type: List(Polynomial(Integer))

axiom

invmatC * vecC

$\label{eq13}\left[{9 \over 5}, \: 3, \:{{15}\over 4}\right]$

(13)

Type: Vector(Fraction(Polynomial(Integer)))

axiom

matPastaA := matrix
[[0,0,80,0,-300],[250,0,-40,0,-300],[250,-250,80,0,0],[250,0,100,-250,0],[0,c1,-200,c2,0]]

$\label{eq14}\left[ \begin{array}{ccccc} 0 & 0 &{80}& 0 & -{300} \ {250}& 0 & -{40}& 0 & -{300} \ {250}& -{250}&{80}& 0 & 0 \ {250}& 0 &{100}& -{250}& 0 \ 0 & c 1 & -{200}& c 2 & 0$

(14)

Type: Matrix(Polynomial(Integer))

axiom

matPastaATimeShift := diagonalMatrix [l1,l2,l3,l4,l5]

$\label{eq15}\left[ \begin{array}{ccccc} l 1 & 0 & 0 & 0 & 0 \ 0 & l 2 & 0 & 0 & 0 \ 0 & 0 & l 3 & 0 & 0 \ 0 & 0 & 0 & l 4 & 0 \ 0 & 0 & 0 & 0 & l 5$

(15)

Type: Matrix(Polynomial(Integer))

axiom

matPastaATimeShift * matPastaA

$\label{eq16}\left[ \begin{array}{ccccc} 0 & 0 &{{80}\ l 1}& 0 & -{{300}\ l 1} \ {{250}\ l 2}& 0 & -{{40}\ l 2}& 0 & -{{300}\ l 2} \ {{250}\ l 3}& -{{250}\ l 3}&{{80}\ l 3}& 0 & 0 \ {{250}\ l 4}& 0 &{{100}\ l 4}& -{{250}\ l 4}& 0 \ 0 &{c 1 \ l 5}& -{{200}\ l 5}&{c 2 \ l 5}& 0$

(16)

Type: Matrix(Polynomial(Integer))

axiom

eqPastaA := determinant (matPastaATimeShift * matPastaA)

$\label{eq17}{\left({{4125000000}\ c 2}+{{3750000000}\ c 1}-{93750000000 0}\right)}\ l 1 \ l 2 \ l 3 \ l 4 \ l 5$

(17)

Type: Polynomial(Integer)

axiom

solve(eqPastaA,c1)

$\label{eq18}\left[{c 1 ={{-{{11}\ c 2}+{2500}}\over{10}}}\right]$

(18)

Type: List(Equation(Fraction(Polynomial(Integer))))

axiom

matPastaB := matrix [[0,0,80,0],[250,0,-40,0],[250,-250,80,0],[250,0,100,-250]]

$\label{eq19}\left[ \begin{array}{cccc} 0 & 0 &{80}& 0 \ {250}& 0 & -{40}& 0 \ {250}& -{250}&{80}& 0 \ {250}& 0 &{100}& -{250}$

(19)

Type: Matrix(Integer)

axiom

invmatPastaB := inverse matPastaB

$\label{eq20}\left[ \begin{array}{cccc} {1 \over{500}}&{1 \over{250}}& 0 & 0 \ {3 \over{500}}&{1 \over{250}}& -{1 \over{250}}& 0 \ {1 \over{80}}& 0 & 0 & 0 \ {7 \over{1000}}&{1 \over{250}}& 0 & -{1 \over{250}}$

(20)

Type: Union(Matrix(Fraction(Integer)),...)

axiom

vecPastaB := [300,300,0,0]

$\label{eq21}\left[{300}, \:{300}, \: 0, \: 0 \right]$

(21)

Type: List(NonNegativeInteger)

axiom

invmatPastaB * vecPastaB

$\label{eq22}\left[{9 \over 5}, \: 3, \:{{15}\over 4}, \:{{33}\over{10}}\right]$

(22)

Type: Vector(Fraction(Integer))

axiom

fmatPasta := matrix
[[1,-1,0,0,0],[0,-1,1,1,0],[0,0,250,0,-c1],[0,0,0,250,-c2],[0,0,0,0,200]]

$\label{eq23}\left[ \begin{array}{ccccc} 1 & - 1 & 0 & 0 & 0 \ 0 & - 1 & 1 & 1 & 0 \ 0 & 0 &{250}& 0 & - c 1 \ 0 & 0 & 0 &{250}& - c 2 \ 0 & 0 & 0 & 0 &{200}$

(23)

Type: Matrix(Polynomial(Integer))

axiom

invfmatPasta := inverse fmatPasta

$\label{eq24}\left[ \begin{array}{ccccc} 1 & - 1 &{1 \over{250}}&{1 \over{250}}&{{c 2 + c 1}\over{5000 0}} \ 0 & - 1 &{1 \over{250}}&{1 \over{250}}&{{c 2 + c 1}\over{5000 0}} \ 0 & 0 &{1 \over{250}}& 0 &{c 1 \over{50000}} \ 0 & 0 & 0 &{1 \over{250}}&{c 2 \over{50000}} \ 0 & 0 & 0 & 0 &{1 \over{200}}$

(24)

Type: Union(Matrix(Fraction(Polynomial(Integer))),...)

axiom

fvecPasta := [0,0,0,0,W]

$\label{eq25}\left[ 0, \: 0, \: 0, \: 0, \: W \right]$

(25)

Type: List(Polynomial(Integer))

axiom

invfmatPasta * fvecPasta

$\label{eq26}\left[{{{W \ c 2}+{W \ c 1}}\over{50000}}, \:{{{W \ c 2}+{W \ c 1}}\over{50000}}, \:{{W \ c 1}\over{50000}}, \:{{W \ c 2}\over{50000}}, \:{W \over{200}}\right]$

(26)

Type: Vector(Fraction(Polynomial(Integer)))

axiom

fmatPastaB := matrix
[[1,-1,0,0,0],[0,-1,1,1,0],[0,0,250,0,-c1],[0,0,0,250,-c2],[80,40,80,100,0]]

$\label{eq27}\left[ \begin{array}{ccccc} 1 & - 1 & 0 & 0 & 0 \ 0 & - 1 & 1 & 1 & 0 \ 0 & 0 &{250}& 0 & - c 1 \ 0 & 0 & 0 &{250}& - c 2 \ {80}&{40}&{80}&{100}& 0$

(27)

Type: Matrix(Polynomial(Integer))

axiom

invfmatPastaB := inverse fmatPastaB

$\label{eq28}\left[ \begin{array}{ccccc} {{{7 \ c 2}+{6 \ c 1}}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{-{5 \ c 2}-{4 \ c 1}}\over{{{11}\ c 2}+{{10}\ c 1}}}&{c 2 \over{{{2750}\ c 2}+{{2500}\ c 1}}}& -{c 1 \over{{{2750}\ c 2}+{{2500}\ c 1}}}&{{c 2 + c 1}\over{{{220}\ c 2}+{{200}\ c 1}}} \ {{-{4 \ c 2}-{4 \ c 1}}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{-{5 \ c 2}-{4 \ c 1}}\over{{{11}\ c 2}+{{10}\ c 1}}}&{c 2 \over{{{2750}\ c 2}+{{2500}\ c 1}}}& -{c 1 \over{{{2750}\ c 2}+{{2500}\ c 1}}}&{{c 2 + c 1}\over{{{220}\ c 2}+{{200}\ c 1}}} \ -{{4 \ c 1}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{6 \ c 1}\over{{{1 1}\ c 2}+{{10}\ c 1}}}&{{{11}\ c 2}\over{{{2750}\ c 2}+{{2 500}\ c 1}}}& -{{{11}\ c 1}\over{{{2750}\ c 2}+{{2500}\ c 1}}}&{c 1 \over{{{220}\ c 2}+{{200}\ c 1}}} \ -{{4 \ c 2}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{6 \ c 2}\over{{{1 1}\ c 2}+{{10}\ c 1}}}& -{c 2 \over{{{275}\ c 2}+{{250}\ c 1}}}&{c 1 \over{{{275}\ c 2}+{{250}\ c 1}}}&{c 2 \over{{{2 20}\ c 2}+{{200}\ c 1}}} \ -{{1000}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{1500}\over{{{11}\ c 2}+{{10}\ c 1}}}& -{{10}\over{{{11}\ c 2}+{{10}\ c 1}}}& -{{11}\over{{{11}\ c 2}+{{10}\ c 1}}}&{{25}\over{{{22}\ c 2}+{{20}\ c 1}}}$

(28)

Type: Union(Matrix(Fraction(Polynomial(Integer))),...)

axiom

invfmatPastaB * fvecPasta

$\label{eq29}\begin{array}{@{}l} \displaystyle \left[{{{W \ c 2}+{W \ c 1}}\over{{{220}\ c 2}+{{200}\ c 1}}}, \:{{{W \ c 2}+{W \ c 1}}\over{{{220}\ c 2}+{{200}\ c 1}}}, \:{{W \ c 1}\over{{{220}\ c 2}+{{200}\ c 1}}}, \: \right. \ \ \displaystyle \left.{{W \ c 2}\over{{{220}\ c 2}+{{200}\ c 1}}}, \:{{{25}\ W}\over{{{22}\ c 2}+{{20}\ c 1}}}\right]$

(29)

Type: Vector(Fraction(Polynomial(Integer)))

axiom

detmatFoodClothes := matrix [[0,0,80,0,0,-300],[250,0,-40,0,0,-300],[250,-250,80,0,0,0],[0,
0,-200,100000,0,0],[0,0,200,50000,-20,0],[0,167 * c1,-200,0,2 * c2,0]]

$\label{eq30}\left[ \begin{array}{cccccc} 0 & 0 &{80}& 0 & 0 & -{300} \ {250}& 0 & -{40}& 0 & 0 & -{300} \ {250}& -{250}&{80}& 0 & 0 & 0 \ 0 & 0 & -{200}&{100000}& 0 & 0 \ 0 & 0 &{200}&{50000}& -{20}& 0 \ 0 &{{167}\ c 1}& -{200}& 0 &{2 \ c 2}& 0$

(30)

Type: Matrix(Polynomial(Integer))

axiom

eqFoodClothes := determinant detmatFoodClothes

$\label{eq31}\begin{array}{@{}l} \displaystyle {{1125000000000000}\ c 2}+{{5010000000000000}\ c 1}- \ \ \displaystyle {7500000000000000}$

(31)

Type: Polynomial(Integer)

axiom

solve(eqFoodClothes,c1)

$\label{eq32}\left[{c 1 ={{-{{75}\ c 2}+{500}}\over{334}}}\right]$

(32)

Type: List(Equation(Fraction(Polynomial(Integer))))

axiom

matFoodClothes := matrix
[[0,0,80,0,0],[250,0,-40,0,0],[250,-250,80,0,0],[0,0,-200,100000,0],[0,0,200,50000,-20]]

$\label{eq33}\left[ \begin{array}{ccccc} 0 & 0 &{80}& 0 & 0 \ {250}& 0 & -{40}& 0 & 0 \ {250}& -{250}&{80}& 0 & 0 \ 0 & 0 & -{200}&{100000}& 0 \ 0 & 0 &{200}&{50000}& -{20}$

(33)

Type: Matrix(Integer)

axiom

invmatFoodClothes := inverse matFoodClothes

$\label{eq34}\left[ \begin{array}{ccccc} {1 \over{500}}&{1 \over{250}}& 0 & 0 & 0 \ {3 \over{500}}&{1 \over{250}}& -{1 \over{250}}& 0 & 0 \ {1 \over{80}}& 0 & 0 & 0 & 0 \ {1 \over{40000}}& 0 & 0 &{1 \over{100000}}& 0 \ {3 \over{16}}& 0 & 0 &{1 \over{40}}& -{1 \over{20}}$

(34)

Type: Union(Matrix(Fraction(Integer)),...)

axiom

vecFoodClothes := [300,300,0,0,0]

$\label{eq35}\left[{300}, \:{300}, \: 0, \: 0, \: 0 \right]$

(35)

Type: List(NonNegativeInteger)

axiom

invmatFoodClothes * vecFoodClothes

$\label{eq36}\left[{9 \over 5}, \: 3, \:{{15}\over 4}, \:{3 \over{400}}, \:{{2 25}\over 4}\right]$

(36)

Type: Vector(Fraction(Integer))