2
$\begingroup$

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]
$\endgroup$

1 Answer 1

3
$\begingroup$

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

$\endgroup$
16
  • $\begingroup$ So you mean there is something wrong in these equations? Please can you indicate more clear? $\endgroup$
    – fhrl
    Jul 7, 2023 at 9:07
  • $\begingroup$ This system dimension is A: [50x50], and b: [50x1]. $\endgroup$
    – fhrl
    Jul 7, 2023 at 9:16
  • 1
    $\begingroup$ "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? $\endgroup$ Jul 7, 2023 at 9:24
  • 4
    $\begingroup$ 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. $\endgroup$ Jul 7, 2023 at 10:18
  • 2
    $\begingroup$ 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). $\endgroup$
    – mikado
    Jul 7, 2023 at 16:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.