Question: how to solve this equations for elements of 3*3 matrix

 

Question

Find t1,t2,t3,...t9 in Matrix
Matrix(3, 3, {(1, 1) = 1+t1, (1, 2) = t2, (1, 3) = t3, (2, 1) = t4, (2, 2) = 1+t5, (2, 3) = t6, (3, 1) = t7, (3, 2) = t8, (3, 3) = t9})

osys := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6) = (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x)
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9],[t1,t2,t3,t4,t5,t6,t7,t8,t9]);

 

since i have only one equation osys, to find t1..t9, i substitute some values into x and y to get enough equation to solve this , however, the result is not expected below

 

then i try without x= 0 or y = 0 , i failed

sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9],[t1,t2,t3,t4,t5,t6,t7,t8,t9]);

 

 

solution : Matrix(3, 3, {(1, 1) = 2, (1, 2) = 0, (1, 3) = 0, (2, 1) = 1, (2, 2) = 1, (2, 3) = 1, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 t1 = 1

t2 = 0

t3 = 0

t4 = 1

t5 = 0

t6 = 1 

t7 = 0

t8 = 0

t9 = 1

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