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Btilde: matrix(
[ -1 , 1/4 + epsilon, 3/4 - epsilon ],
[ 1/10 - epsilon, -1 , 1/4 + epsilon ],
[ 9/10 + epsilon, 3/4 - epsilon, -1 ]
);
r: expand(Btilde[1] / Btilde[1,1]);
Btilde[1]: r;
Btilde[2]: Btilde[2] - Btilde[2,1] * r;
Btilde[3]: Btilde[3] - Btilde[3,1] * r;
Btilde: expand(Btilde);
r: Btilde[2] / Btilde[2,2];
Btilde[2]: r;
Btilde[3]: Btilde[3] - Btilde[3,2] * r;
Btilde: ratsimp(expand(Btilde));
Btilde[1]: Btilde[1] - Btilde[1,2] * Btilde[2];
Btilde: ratsimp(expand(Btilde));
l: 78 + 12 * epsilon + 80 * epsilon^2;
D: ratsimp(expand(l*Btilde));
n: ratsimp(expand(l -D[1,3] -D[2,3]));
p: (1/n) * matrix(
[ -Btilde[1,3]*l ],
[ -Btilde[2,3]*l ],
[ l ]
);
p: ratsimp(expand(p));
taylor(p, epsilon, 0, 3);
G: matrix(
[ 0, 1, -1 ],
[ -1, 0, 1 ],
[ 1, -1, 0 ]
);
e: matrix([1,1,1]);
ratsimp(expand(e. (G*Btilde) . p));
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