# Does the solution exist in this matrix system?

I got these equations after the post process, so I just listed the numerical equations, and there are 50 equations total with 50 unknown variables, however, the Solve and NSolve cannot get the solution.

So is this system (maybe linear) have the solution, and how to decompose the system to Ax=b and how to extract matrix A and matrix b to judge its rank or use the LinearSolve to solve this system?

By the way, as I cannot use all symbolic calculations to get the equation, for example, initially when assigning the values, I use 13/10 rather than 1.3 to do the calculation, so but the MatrixExp is and Inverse is very slow and cannot carry on when the matrix size is bigger, so I finally I used the input values in the style of 1.3, and after several calculations to get the 50 equations. In this process, I suspect that Mathematica has changed the accuracy of the equation, for example, I do not know what the following accuracy will affect the final result, and I just copy the equations from Mathematica notebook.

**{(4.763351335421033*^-18 - 5.757948863725194*^-17 I) + 0.0398837643080161 aIVcoefficient[1] - 0.07942645028395248 aIVcoefficient[2] + 1. aIVcoefficient[3]**


The above will lost the accuracy, but maybe no better way?

The following is the code:

   equa = {{(0. + 0. I) + 0.6815984732601709 aIcoefficient[1] -
0.6815984732601709 aIIcoefficient[1] +
1.467139436532002 bIcoefficient[1] -
1.467139436532002 bIIcoefficient[1]}, {(0.8073527509320696 +
0.12787211360085063 I) +
0.8255897729866637 aIcoefficient[2] -
0.8255897729866637 aIIcoefficient[2] +
1.2112553143462372 bIcoefficient[2] -
1.2112553143462372 bIIcoefficient[2]}, {(0. + 0. I) +
1. aIcoefficient[3] - 1. aIIcoefficient[3] +
1. bIcoefficient[3] -
1. bIIcoefficient[3]}, {(0.8073527509320696 -
0.12787211360085063 I) +
0.8255897729866637 aIcoefficient[4] -
0.8255897729866637 aIIcoefficient[4] +
1.2112553143462372 bIcoefficient[4] -
1.2112553143462372 bIIcoefficient[4]}, {(0. + 0. I) +
0.6815984732601709 aIcoefficient[5] -
0.6815984732601709 aIIcoefficient[5] +
1.467139436532002 bIcoefficient[5] -
1.467139436532002 bIIcoefficient[5]}, {0. +
24459.924740303326 aIcoefficient[1] -
2.4459924740303326*^7 aIIcoefficient[1] -
52649.94217116712 bIcoefficient[1] +
5.264994217116712*^7 bIIcoefficient[1]}, {0. +
14813.606915100705 aIcoefficient[2] -
1.4813606915100705*^7 aIIcoefficient[2] -
21733.62690242742 bIcoefficient[2] +
2.1733626902427416*^7 bIIcoefficient[2]}, {0.}, {0. +
14813.606915100705 aIcoefficient[4] -
1.4813606915100705*^7 aIIcoefficient[4] -
21733.62690242742 bIcoefficient[4] +
2.1733626902427416*^7 bIIcoefficient[4]}, {0. +
24459.924740303326 aIcoefficient[5] -
2.4459924740303326*^7 aIIcoefficient[5] -
52649.94217116712 bIcoefficient[5] +
5.264994217116712*^7 bIIcoefficient[5]}, {(0. + 0. I) +
0.544006716016415 aIIcoefficient[1] -
0.544006716016415 aIIIcoefficient[1] +
1.8382126002463282 bIIcoefficient[1] -
1.8382126002463282 bIIIcoefficient[
1]}, {(-0.8073527509320696 - 0.12787211360085063 I) +
0.7375681094084905 aIIcoefficient[2] -
0.7375681094084905 aIIIcoefficient[2] +
1.3558069922545495 bIIcoefficient[2] -
1.3558069922545495 bIIIcoefficient[2]}, {(0. + 0. I) +
1. aIIcoefficient[3] - 1. aIIIcoefficient[3] +
1. bIIcoefficient[3] -
1. bIIIcoefficient[3]}, {(-0.8073527509320696 +
0.12787211360085063 I) +
0.7375681094084905 aIIcoefficient[4] -
0.7375681094084905 aIIIcoefficient[4] +
1.3558069922545495 bIIcoefficient[4] -
1.3558069922545495 bIIIcoefficient[4]}, {(0. + 0. I) +
0.544006716016415 aIIcoefficient[5] -
0.544006716016415 aIIIcoefficient[5] +
1.8382126002463282 bIIcoefficient[5] -
1.8382126002463282 bIIIcoefficient[5]}, {0. +
1.952229040117281*^7 aIIcoefficient[1] -
1.952229040117281*^7 aIIIcoefficient[1] -
6.59663183276233*^7 bIIcoefficient[1] +
6.59663183276233*^7 bIIIcoefficient[1]}, {0. +
1.3234228915366983*^7 aIIcoefficient[2] -
1.3234228915366983*^7 aIIIcoefficient[2] -
2.4327326346771885*^7 bIIcoefficient[2] +
2.4327326346771885*^7 bIIIcoefficient[2]}, {0.}, {0. +
1.3234228915366983*^7 aIIcoefficient[4] -
1.3234228915366983*^7 aIIIcoefficient[4] -
2.4327326346771885*^7 bIIcoefficient[4] +
2.4327326346771885*^7 bIIIcoefficient[4]}, {0. +
1.952229040117281*^7 aIIcoefficient[5] -
1.952229040117281*^7 aIIIcoefficient[5] -
6.59663183276233*^7 bIIcoefficient[5] +
6.59663183276233*^7 bIIIcoefficient[
5]}, {0.527102228842787 aIIIcoefficient[1] -
0.902104931583961 aIVcoefficient[1] -
0.03810467543486388 aIVcoefficient[2] +
1.9796065676594032*^-18 aIVcoefficient[3] +
0.03225197484587826 aIVcoefficient[4] -
0.013436568705534946 aIVcoefficient[5] +
1.89716518974967 bIIIcoefficient[1] -
1.113571355149769 bIVcoefficient[1] +
0.052510035946752916 bIVcoefficient[2] -
1.1669034626942133*^-18 bIVcoefficient[3] -
0.044892482120949935 bIVcoefficient[4] +
0.020335107226451044 bIVcoefficient[
5]}, {0.7260180637165904 aIIIcoefficient[2] -
0.09863741283654497 aIVcoefficient[1] -
0.8295030028081504 aIVcoefficient[2] +
2.9447225657865545*^-17 aIVcoefficient[3] -
0.010449635327188143 aIVcoefficient[4] -
0.019924873066124338 aIVcoefficient[5] +
1.3773761976125731 bIIIcoefficient[2] +
0.13164233320918256 bIVcoefficient[1] -
1.2109503935218189 bIVcoefficient[2] -
3.507565804313883*^-17 bIVcoefficient[3] +
0.0193318317698859 bIVcoefficient[4] +
0.022671830114584512 bIVcoefficient[5]}, {1. aIIIcoefficient[
3] - 0.03494831300401707 aIVcoefficient[1] +
0.06856891768501899 aIVcoefficient[2] -
1.0000000000000002 aIVcoefficient[3] +
0.0685689176850185 aIVcoefficient[4] -
0.03494831300401713 aIVcoefficient[5] +
1. bIIIcoefficient[3] +
0.04878791774234126 bIVcoefficient[1] -
0.08197421572813807 bIVcoefficient[2] -
1.0000000000000002 bIVcoefficient[3] -
0.08197421572813762 bIVcoefficient[4] +
0.04878791774234126 bIVcoefficient[
5]}, {0.7260180637165904 aIIIcoefficient[4] -
0.019924873066123804 aIVcoefficient[1] -
0.010449635327188313 aIVcoefficient[2] +
1.2828468405456788*^-17 aIVcoefficient[3] -
0.8295030028081509 aIVcoefficient[4] -
0.09863741283654433 aIVcoefficient[5] +
1.3773761976125731 bIIIcoefficient[4] +
0.022671830114583937 bIVcoefficient[1] +
0.01933183176988634 bIVcoefficient[2] -
1.4485740430212436*^-17 bIVcoefficient[3] -
1.2109503935218184 bIVcoefficient[4] +
0.13164233320918195 bIVcoefficient[
5]}, {0.527102228842787 aIIIcoefficient[5] -
0.013436568705534948 aIVcoefficient[1] +
0.03225197484587825 aIVcoefficient[2] +
3.3024962924608757*^-18 aIVcoefficient[3] -
0.03810467543486375 aIVcoefficient[4] -
0.9021049315839611 aIVcoefficient[5] +
1.89716518974967 bIIIcoefficient[5] +
0.02033510722645093 bIVcoefficient[1] -
0.04489248212094991 bIVcoefficient[2] -
4.285645474198178*^-18 bIVcoefficient[3] +
0.05251003594675275 bIVcoefficient[4] -
1.1135713551497688 bIVcoefficient[5]}, {0. +
1.8915653942521974*^7 aIIIcoefficient[1] -
4.808151902260667*^6 aIVcoefficient[1] +
3.9455190357605047*^6 aIVcoefficient[2] +
5.014167210139676*^-10 aIVcoefficient[3] -
651517.4822687587 aIVcoefficient[4] -
421069.88318322925 aIVcoefficient[5] -
6.808189804070656*^7 bIIIcoefficient[1] +
7.144448826363817*^6 bIVcoefficient[1] -
6.394654832194837*^6 bIVcoefficient[2] -
7.754025181791637*^-10 bIVcoefficient[3] +
1.6224348101310125*^6 bIVcoefficient[4] +
272900.58979143936 bIVcoefficient[5]}, {0. +
1.30269857513531*^7 aIIIcoefficient[2] +
3.9455190357604977*^6 aIVcoefficient[1] -
5.1726437672463795*^6 aIVcoefficient[2] -
6.085056089984946*^-10 aIVcoefficient[3] +
2.814432666158135*^6 aIVcoefficient[4] -
651517.4822687613 aIVcoefficient[5] -
2.4714343894832052*^7 bIIIcoefficient[2] -
6.39465483219483*^6 bIVcoefficient[1] +
8.320611019494848*^6 bIVcoefficient[2] +
9.220637370463883*^-10 bIVcoefficient[3] -
4.911953674228196*^6 bIVcoefficient[4] +
1.6224348101310069*^6 bIVcoefficient[5]}, {0. +
7.421294256748206*^-9 aIVcoefficient[1] -
4.947529504498804*^-9 aIVcoefficient[2] +
1.2348119723278187*^-10 aIVcoefficient[3] +
3.003857199159988*^-9 aIVcoefficient[4] +
1.117611575569819*^-8 aIVcoefficient[5] -
9.54166404439055*^-9 bIVcoefficient[1] +
7.774689221355263*^-9 bIVcoefficient[2] -
1.2348119723278164*^-10 bIVcoefficient[3] -
4.240739575284689*^-9 bIVcoefficient[4] -
1.2898916208157596*^-8 bIVcoefficient[5]}, {0. +
1.30269857513531*^7 aIIIcoefficient[4] -
651517.4822687615 aIVcoefficient[1] +
2.814432666158148*^6 aIVcoefficient[2] -
2.427150337247048*^-10 aIVcoefficient[3] -
5.172643767246372*^6 aIVcoefficient[4] +
3.9455190357604926*^6 aIVcoefficient[5] -
2.4714343894832052*^7 bIIIcoefficient[4] +
1.622434810131026*^6 bIVcoefficient[1] -
4.911953674228223*^6 bIVcoefficient[2] +
1.4696843914103367*^-10 bIVcoefficient[3] +
8.320611019494826*^6 bIVcoefficient[4] -
6.394654832194806*^6 bIVcoefficient[5]}, {0. +
1.8915653942521974*^7 aIIIcoefficient[5] -
421069.8831832276 aIVcoefficient[1] -
651517.4822687629 aIVcoefficient[2] +
4.5726499919469627*^-10 aIVcoefficient[3] +
3.945519035760497*^6 aIVcoefficient[4] -
4.808151902260664*^6 aIVcoefficient[5] -
6.808189804070656*^7 bIIIcoefficient[5] +
272900.58979142876 bIVcoefficient[1] +
1.6224348101310222*^6 bIVcoefficient[2] -
4.805916489969915*^-10 bIVcoefficient[3] -
6.3946548321948135*^6 bIVcoefficient[4] +
7.144448826363801*^6 bIVcoefficient[
5]}, {(-0.0017322378178796418 - 0.026907023612397867 I) +
0.8862731430073842 aIVcoefficient[1] +
0.0435910038025796 aIVcoefficient[2] -
2.392167074317305*^-18 aIVcoefficient[3] -
0.036864563217668886 aIVcoefficient[4] +
0.015234287295908198 aIVcoefficient[5] -
0.7818791967905447 aVcoefficient[1] +
0.0567718703104632 aVcoefficient[2] +
1.781270791572057*^-17 aVcoefficient[3] -
0.024450167285175826 aVcoefficient[4] -
0.013896267538051722 aVcoefficient[5] +
1.1354410995353608 bIVcoefficient[1] -
0.06355943603318351 bIVcoefficient[2] +
1.2646135041853175*^-18 bIVcoefficient[3] +
0.054388877086034515 bIVcoefficient[4] -
0.024801777692165558 bIVcoefficient[5] -
1.3093308558303136 bVcoefficient[1] -
0.09629591944572383 bVcoefficient[2] +
4.511148910838657*^-18 bVcoefficient[3] +
0.04425288414665807 bVcoefficient[4] +
0.04332308517158867 bVcoefficient[
5]}, {(-0.03828217746866802 - 0.0843441425243542 I) +
0.11313655266643213 aIVcoefficient[1] +
0.8030327158896496 aIVcoefficient[2] -
3.412739005320015*^-17 aIVcoefficient[3] +
0.011601315983215059 aIVcoefficient[4] +
0.023125700905252122 aIVcoefficient[5] +
0.2097356768238431 aVcoefficient[1] -
0.7839756217397915 aVcoefficient[2] +
3.0684623915111367*^-17 aVcoefficient[3] -
0.002287649719937317 aVcoefficient[4] -
0.06643270656660281 aVcoefficient[5] -
0.158865449095193 bIVcoefficient[1] +
1.2530134394042658 bIVcoefficient[2] +
4.1922545531818625*^-17 bIVcoefficient[3] -
0.023934415137685572 bIVcoefficient[4] -
0.026909034879838156 bIVcoefficient[5] -
0.3543147903282006 bVcoefficient[1] -
1.3051311328355724 bVcoefficient[2] -
1.9221849581814614*^-17 bVcoefficient[3] +
0.023807232675295054 bVcoefficient[4] +
0.12357442575880696 bVcoefficient[
5]}, {(4.763351335421033*^-18 - 5.757948863725194*^-17 I) +
0.0398837643080161 aIVcoefficient[1] -
0.07942645028395248 aIVcoefficient[2] + 1. aIVcoefficient[3] -
0.07942645028395198 aIVcoefficient[4] +
0.039883764308016156 aIVcoefficient[5] -
0.020402081708550294 aVcoefficient[1] +
0.1746125536318779 aVcoefficient[2] -
1.0000000000000002 aVcoefficient[3] +
0.1746125536318778 aVcoefficient[4] -
0.020402081708552733 aVcoefficient[5] -
0.05905188475907842 bIVcoefficient[1] +
0.0979871404275791 bIVcoefficient[2] + 1. bIVcoefficient[3] +
0.09798714042757863 bIVcoefficient[4] -
0.0590518847590783 bIVcoefficient[5] -
0.014460970302774045 bVcoefficient[1] -
0.22267345197801064 bVcoefficient[2] -
1.0000000000000002 bVcoefficient[3] -
0.22267345197800925 bVcoefficient[4] -
0.014460970302769603 bVcoefficient[
5]}, {(-0.03828217746866845 + 0.08434414252435436 I) +
0.02312570090525179 aIVcoefficient[1] +
0.011601315983215277 aIVcoefficient[2] -
1.4926070905077245*^-17 aIVcoefficient[3] +
0.8030327158896501 aIVcoefficient[4] +
0.11313655266643143 aIVcoefficient[5] -
0.06643270656660208 aVcoefficient[1] -
0.0022876497199371395 aVcoefficient[2] -
9.152794752285988*^-17 aVcoefficient[3] -
0.7839756217397928 aVcoefficient[4] +
0.20973567682384162 aVcoefficient[5] -
0.026909034879837847 bIVcoefficient[1] -
0.023934415137686238 bIVcoefficient[2] +
1.7217694314674187*^-17 bIVcoefficient[3] +
1.253013439404265 bIVcoefficient[4] -
0.15886544909519204 bIVcoefficient[5] +
0.1235744257588055 bVcoefficient[1] +
0.02380723267529489 bVcoefficient[2] -
2.220522317085354*^-17 bVcoefficient[3] -
1.3051311328355697 bVcoefficient[4] -
0.35431479032819757 bVcoefficient[
5]}, {(-0.0017322378178794388 + 0.02690702361239803 I) +
0.0152342872959082 aIVcoefficient[1] -
0.03686456321766886 aIVcoefficient[2] -
3.79996469960318*^-18 aIVcoefficient[3] +
0.043591003802579485 aIVcoefficient[4] +
0.8862731430073844 aIVcoefficient[5] -
0.013896267538051532 aVcoefficient[1] -
0.02445016728517598 aVcoefficient[2] +
1.0055530360521509*^-16 aVcoefficient[3] +
0.05677187031046276 aVcoefficient[4] -
0.7818791967905452 aVcoefficient[5] -
0.024801777692165416 bIVcoefficient[1] +
0.05438887708603458 bIVcoefficient[2] +
5.1627638746858775*^-18 bIVcoefficient[3] -
0.06355943603318337 bIVcoefficient[4] +
1.1354410995353605 bIVcoefficient[5] +
0.04332308517158823 bVcoefficient[1] +
0.04425288414665826 bVcoefficient[2] -
1.7166789232538527*^-17 bVcoefficient[3] -
0.09629591944572274 bVcoefficient[4] -
1.309330855830312 bVcoefficient[
5]}, {4.646751185471299*^6 aIVcoefficient[1] -
3.780945048645965*^6 aIVcoefficient[2] -
4.827249369520237*^-10 aIVcoefficient[3] +
592771.5660010556 aIVcoefficient[4] +
424926.4542889232 aIVcoefficient[5] -
340250.5153765599 aVcoefficient[1] +
160852.02024063247 aVcoefficient[2] -
5.495451723404348*^-11 aVcoefficient[3] -
129052.44118121795 aVcoefficient[4] +
204066.9736389931 aVcoefficient[5] -
7.403000687430209*^6 bIVcoefficient[1] +
6.671936269206717*^6 bIVcoefficient[2] +
8.060078235187699*^-10 bIVcoefficient[3] -
1.7415169013702518*^6 bIVcoefficient[4] -
247425.38813345888 bIVcoefficient[5] +
94838.28041971105 bVcoefficient[1] -
44677.45386916875 bVcoefficient[2] +
3.242646313370151*^-11 bVcoefficient[3] +
23730.524379016948 bVcoefficient[4] -
35094.97727966463 bVcoefficient[
5]}, {-3.7809450486459574*^6 aIVcoefficient[1] +
4.962408758996038*^6 aIVcoefficient[2] +
5.871766352214633*^-10 aIVcoefficient[3] -
2.6794448759045843*^6 aIVcoefficient[4] +
592771.5660010569 aIVcoefficient[5] +
160852.02024063512 aVcoefficient[1] -
101538.70755824399 aVcoefficient[2] +
6.36591010227174*^-11 aVcoefficient[3] +
72933.57637043372 aVcoefficient[4] -
129052.44118121683 aVcoefficient[5] +
6.671936269206713*^6 bIVcoefficient[1] -
8.679007297767732*^6 bIVcoefficient[2] -
9.57219217837519*^-10 bIVcoefficient[3] +
5.157985077441051*^6 bIVcoefficient[4] -
1.7415169013702462*^6 bIVcoefficient[5] -
71571.09659449034 bVcoefficient[1] +
31821.95762665411 bVcoefficient[2] -
4.4076038659483016*^-11 bVcoefficient[3] -
6716.420210295398 bVcoefficient[4] +
1519.973256862665 bVcoefficient[
5]}, {-7.067899292141148*^-9 aIVcoefficient[1] +
4.947529504498803*^-9 aIVcoefficient[2] -
1.2348119723278202*^-10 aIVcoefficient[3] -
3.4014265343429277*^-9 aIVcoefficient[4] -
1.1220290126274072*^-8 aIVcoefficient[5] -
4.947529504498803*^-9 aVcoefficient[1] +
2.1203697876423445*^-9 aVcoefficient[2] -
6.147334204074303*^-11 aVcoefficient[3] -
4.417437057588218*^-9 aVcoefficient[4] +
2.1203697876423445*^-9 aVcoefficient[5] +
9.895059008997607*^-9 bIVcoefficient[1] -
6.361109362927034*^-9 bIVcoefficient[2] +
1.2348119723278164*^-10 bIVcoefficient[3] +
4.240739575284689*^-9 bIVcoefficient[4] +
1.3163962431612888*^-8 bIVcoefficient[5] +
36881.867243375134 bVcoefficient[1] -
13276.604734541737 bVcoefficient[2] +
5.1405592897502476*^-11 bVcoefficient[3] -
13276.604734534103 bVcoefficient[4] +
36881.86724337187 bVcoefficient[
5]}, {592771.5660010583 aIVcoefficient[1] -
2.679444875904597*^6 aIVcoefficient[2] +
2.484361054137977*^-10 aIVcoefficient[3] +
4.962408758996029*^6 aIVcoefficient[4] -
3.780945048645952*^6 aIVcoefficient[5] -
129052.4411812103 aVcoefficient[1] +
72933.57637042785 aVcoefficient[2] +
5.179665112159971*^-11 aVcoefficient[3] -
101538.70755823726 aVcoefficient[4] +
160852.02024062825 aVcoefficient[5] -
1.7415169013702658*^6 bIVcoefficient[1] +
5.15798507744108*^6 bIVcoefficient[2] -
1.351054798740686*^-10 bIVcoefficient[3] -
8.679007297767706*^6 bIVcoefficient[4] +
6.671936269206684*^6 bIVcoefficient[5] +
1519.9732568598183 bVcoefficient[1] -
6716.420210288418 bVcoefficient[2] -
5.2790866798381914*^-11 bVcoefficient[3] +
31821.957626646723 bVcoefficient[4] -
71571.09659448701 bVcoefficient[
5]}, {424926.4542889205 aIVcoefficient[1] +
592771.5660010596 aIVcoefficient[2] -
4.5474776083295977*^-10 aIVcoefficient[3] -
3.780945048645958*^6 aIVcoefficient[4] +
4.646751185471296*^6 aIVcoefficient[5] +
204066.9736389881 aVcoefficient[1] -
129052.44118121365 aVcoefficient[2] -
3.2082460409503426*^-11 aVcoefficient[3] +
160852.02024062644 aVcoefficient[4] -
340250.5153765538 aVcoefficient[5] -
247425.38813344805 bIVcoefficient[1] -
1.741516901370262*^6 bIVcoefficient[2] +
4.81898320148912*^-10 bIVcoefficient[3] +
6.671936269206694*^6 bIVcoefficient[4] -
7.40300068743019*^6 bIVcoefficient[5] -
35094.97727966243 bVcoefficient[1] +
23730.524379011324 bVcoefficient[2] +
4.790753019328496*^-11 bVcoefficient[3] -
44677.45386916243 bVcoefficient[4] +
94838.28041970811 bVcoefficient[5]}, {1. aIcoefficient[1] +
1. bIcoefficient[1]}, {1. aIcoefficient[2] +
1. bIcoefficient[2]}, {1. aIcoefficient[3] +
1. bIcoefficient[3]}, {1. aIcoefficient[4] +
1. bIcoefficient[4]}, {1. aIcoefficient[5] +
1. bIcoefficient[5]}, {(-1.2133945259254957 +
0.07811669979164113 I) + (0. +
27.72502160734832 I) aVcoefficient[
1] - (0. + 4.068360294401766 I) aVcoefficient[
2] - (0. + 3.060402098430089*^-16 I) aVcoefficient[
3] + (0. + 1.7157479167334777 I) aVcoefficient[
4] + (0. + 0.558656889210907 I) aVcoefficient[
5] + (0. + 81.08978940071115 I) bVcoefficient[
1] + (0. + 12.202478345059541 I) bVcoefficient[
2] - (0. + 4.881152774367718*^-16 I) bVcoefficient[
3] - (0. + 5.872668419489061 I) bVcoefficient[
4] - (0. + 6.854120705090718 I) bVcoefficient[
5]}, {(-1.901784498858043 +
0.8631832574671483 I) - (0. +
7.524393801411527 I) aVcoefficient[
1] + (0. + 13.933415009563763 I) aVcoefficient[
2] - (0. + 1.0146543872206155*^-15 I) aVcoefficient[
3] - (0. + 0.13775960352412106 I) aVcoefficient[
4] + (0. + 2.3090692666855874 I) aVcoefficient[
5] + (0. + 22.380656530476674 I) bVcoefficient[
1] + (0. + 40.24812651369694 I) bVcoefficient[
2] + (0. + 9.408143479383613*^-16 I) bVcoefficient[
3] - (0. + 2.1988688929825155 I) bVcoefficient[
4] - (0. + 8.348590169549814 I) bVcoefficient[5]}, {0. +
0. I}, {(-1.9017844988580466 -
0.863183257467158 I) - (0. +
2.3090692666855674 I) aVcoefficient[
1] + (0. + 0.1377596035241246 I) aVcoefficient[
2] - (0. + 1.7389583178924158*^-15 I) aVcoefficient[
3] - (0. + 13.933415009563806 I) aVcoefficient[
4] + (0. + 7.5243938014114855 I) aVcoefficient[
5] + (0. + 8.348590169549723 I) bVcoefficient[
1] + (0. + 2.198868892982503 I) bVcoefficient[
2] - (0. + 1.3713357189750004*^-15 I) bVcoefficient[
3] - (0. + 40.248126513696754 I) bVcoefficient[
4] - (0. + 22.380656530476436 I) bVcoefficient[
5]}, {(-1.213394525925503 -
0.07811669979163197 I) - (0. +
0.5586568892108987 I) aVcoefficient[
1] - (0. + 1.7157479167334848 I) aVcoefficient[
2] + (0. + 4.3806228247859174*^-15 I) aVcoefficient[
3] + (0. + 4.068360294401739 I) aVcoefficient[
4] - (0. + 27.725021607348335 I) aVcoefficient[
5] + (0. + 6.854120705090679 I) bVcoefficient[
1] + (0. + 5.872668419489085 I) bVcoefficient[
2] - (0. + 1.955539387118312*^-15 I) bVcoefficient[
3] - (0. + 12.202478345059394 I) bVcoefficient[
4] - (0. + 81.08978940071094 I) bVcoefficient[5]}};
equaRight = Transpose[{Table[0, {eqauRightIndex, 1, (2*NN + 1)*10}]}]
varibales = {aIcoefficient[1], aIcoefficient[2], aIcoefficient[3],
aIcoefficient[4], aIcoefficient[5], aIIcoefficient[1],
aIIcoefficient[2], aIIcoefficient[3], aIIcoefficient[4],
aIIcoefficient[5], aIIIcoefficient[1], aIIIcoefficient[2],
aIIIcoefficient[3], aIIIcoefficient[4], aIIIcoefficient[5],
aIVcoefficient[1], aIVcoefficient[2], aIVcoefficient[3],
aIVcoefficient[4], aIVcoefficient[5], aVcoefficient[1],
aVcoefficient[2], aVcoefficient[3], aVcoefficient[4],
aVcoefficient[5], bIcoefficient[1], bIcoefficient[2],
bIcoefficient[3], bIcoefficient[4], bIcoefficient[5],
bIIcoefficient[1], bIIcoefficient[2], bIIcoefficient[3],
bIIcoefficient[4], bIIcoefficient[5], bIIIcoefficient[1],
bIIIcoefficient[2], bIIIcoefficient[3], bIIIcoefficient[4],
bIIIcoefficient[5], bIVcoefficient[1], bIVcoefficient[2],
bIVcoefficient[3], bIVcoefficient[4], bIVcoefficient[5],
bVcoefficient[1], bVcoefficient[2], bVcoefficient[3],
bVcoefficient[4], bVcoefficient[5]};
NSolve[equa == equaRight, varibales]


Apparently, your system has a 5-dimensional null space:

x = varibales;
A = N[D[equa[[All, 1]], {x, 1}]];
b = equa[[All, 1]] - A . x;
nullspace = NullSpace[A];
Length[nullspace]


5

• So you mean there is something wrong in these equations? Please can you indicate more clear?
– fhrl
Jul 7, 2023 at 9:07
• This system dimension is A: [50x50], and b: [50x1].
– fhrl
Jul 7, 2023 at 9:16
• "So you mean there is something wrong in these equations? " Yes. "Please can you indicate more clear?" No. How much clearer do you want it? Jul 7, 2023 at 9:24
• If A has a null space of 5 it means the Determinant is zero and it does not have an inverse. Therefore, the equations are underdetermined. The best you may get is 45 variables as functions of the 5 additional variables. Jul 7, 2023 at 10:18
• In (I hope) simple terms, 5 of your equations are effectively linear combinations of the other 45. These equations either make it impossible to find a solution (think of x+y==1&&x+y==2) or give an infinite number of solutions (think of x+y==1&&2x+2y==2). Jul 7, 2023 at 16:04