# solve equations with vector parameter

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Heba Amin Saleh on 23 Sep 2020
Answered: Nikhil Sonavane on 30 Sep 2020
I have to solve 5 equations with 5 unkown . these equations have vectors parameters and each unknown is expected to be vectors also. when i try to solve the equation the output of unkown is (0x1 sym)
X11=1;
X12=0;
X13=[0.0387,0.0794,0.1213,0.1643,0.2085,0.2539,0.3005,0.3483,0.3974,0.4477,0.4992,0.5519,0.6058,0.6607,0.7163,0.7722,0.8278];
X14=-1;
X15=0;
X21=0;
X22=1;
X23=[ 0.9993,0.9968,0.9926,0.9864,0.9780,0.9672,0.9538,0.9374,0.9176,0.8942,0.8665,0.8339,0.7956,0.7507,0.6978,0.6353,0.5610];
X24=0;
X25=-1;
X31=0;
X32=0;
X33=[31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317,31.5317];
X34=[32.2796,30.2166,28.0633,25.8279,23.5195,21.1478,18.7231,16.2560,13.7576,11.2389,8.7111,6.1851,3.6715,1.1805,-1.2782,-3.6956,-6.0637];
X35=-[38.1842,39.8366,41.3818,42.8126,44.1229,45.3075,46.3621,47.2836,48.0700,48.7205,49.2353,49.6160,49.8650,49.9861,49.9837,49.8632,49.6310];
X41=X34;
X42=-X35;
X43=[26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486,26.3486];
X44=0;
X45=0;
X51=[14.5000,15.9594,17.3780,18.7496,20.0686,21.3294,22.5273,23.6577,24.7169,25.7017,26.6097,27.4389,28.1885,28.8580,29.4478,29.9588,30.3928];
X52=-1*[28.0,27.1946,26.3108,25.3516,24.3208,23.2230,22.0629,20.8462,19.5787,18.2667,16.9167,15.5356,14.1301,12.7070,11.2730,9.8346,8.3982];
X53=0;
X54=-1*[14.50,13.3171,12.0937,10.8345,9.5447,8.2295,6.8948,5.5462,4.1897,2.8311,1.4763,0.1307,-1.2001,-2.5110,-3.7974,-5.0547,-6.2793];
X55=[22.0,22.7355,23.4092,24.018,24.5591,25.0305,25.4305,25.7583,26.0134,26.1961,26.3072,26.3483,26.3213,26.2287,26.0736,25.8592,25.5895];
z1=-1*[2.4818,2.5235,2.5716,2.6275,2.6926,2.7691,2.8596,2.9678,3.0989,3.2601,3.4621,3.7215,4.0655,4.5414,5.2402,6.3617,8.4471];
z2=[-2.0428,-2.1909,-2.3569,-2.5444,-2.7577,-3.0027,-3.2870,-3.6210,-4.0192,-4.5020,-5.0999,-5.8599,-6.8586,-8.2300,-10.2317,-13.4291,-19.3536];
z3=[-33.1082,-34.4209,-35.9295,-37.6723,-39.6983,-42.0711,-44.8749,-48.2233,-52.2738,-57.2515,-63.4889,-71.4998,-82.1215,-96.8185,-118.4038,-153.0558,-217.5021];
z4=[-136.6115,-139.4838,-143.2967,-148.2598,-154.6319,-162.7373,-172.9912,-185.9396,-202.3232,-223.1840,-250.0492,-285.2668,-332.6579,-398.9024,-496.8369,-654.6707,-948.8008];
z5=[8.9562,16.2057,24.0730,32.6428,42.0260,52.3699,63.8735,76.8111,91.5687,108.7046,129.0528,153.9109,185.4051,227.2661,286.6752,379.4241,548.2897];
syms y1 y2 y3 y4 y5
eq1= (X11*y1)+(X12*y2)+(X13*y3)+(X14*y4)+(X15*y5) == z1;
eq2= (X21*y1)+(X22*y2)+(X23*y3)+(X24*y4)+(X25*y5) == z2;
eq3= (X31*y1)+(X32*y2)+(X33*y3)+(X34*y4)+(X35*y5) == z3;
eq4= (X41*y1)+(X42*y2)+(X43*y3)+(X44*y4)+(X45*y5) == z4;
eq5= (X51*y1)+(X52*y2)+(X53*y3)+(X54*y4)+(X55*y5) == z5;
eq1=subs(eq1); eq2=subs(eq2); eq3=subs(eq3); eq4=subs(eq4); eq5=subs(eq5);
[y1,y2,y3,y4,y5] = vpasolve([eq1,eq2,eq3,eq4,eq5], [y1,y2,y3,y4,y5]);

Nikhil Sonavane on 30 Sep 2020
In my opinion, here vpsolve is not able to find a solution. When vpasolve cannot find a solution, it returns an empty object. Provide initial guess to help the solver finding a solution. For an example, see Provide Initial Guess to Find Solutions

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