how to solve matrix equation?

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Nara Lee
Nara Lee 2021-4-18
回答： Nara Lee 2021-4-24
I want to solve a equation which has vector known elements and obvisouly the answer should be vector too.
x1=sym('x1',[121 1]);
x2=sym('x2',[121 1]);
s=solve(x1+x2==n1,x1.*x2==n2,[x1,x2]);
but I think I didn't write the right code coz it's been a long time that is busy and there is no answer yet. I really need your help.

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采纳的回答

Walter Roberson
Walter Roberson 2021-4-22
x1+x2=n1
x1*x2=n2
so
x2 = n1-x1
x1*(n1-x1) = n2
x1*n1-x1^2 = n2
x1^2 - x1*n1 + n2 = 0
and solve the quadratic to get x1 and then x2. There will be two solutions
Do this just for scalars to get the forms of the solutions. Then substitute in the vectors.
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Nara Lee
Nara Lee 2021-4-24
the thing is I have a matrix that is not square matrix[242 2]
and i want it to be inverse then i thought if A*A(inv)=1
So I create a matrix [242 2] that gives me what i want when A*A(inv) is done. then u*x=my creation would give me x that is my inverse matrix
and i ran your code and it didn't work.
Walter Roberson
Walter Roberson 2021-4-24
Ran in:
format long g
A = rand(42,2);
Ainv = pinv(A);
Ainv * A
ans = 2×2
1 -5.20417042793042e-17 -1.38777878078145e-16 1
ans = 42×42
0.122279499034516 0.100591415380188 0.0828882943136175 0.00950733225267564 0.0643791627164946 -0.0495366330834786 0.0323927791469979 0.0810689532034453 0.00723859743041875 0.0614055106488573 0.0281472612408997 0.0103958103260886 0.00419121852178334 0.000443856252444105 0.0633644133018594 0.0572660502092225 -0.0254592276700414 -0.0671865361348825 0.0356470256968464 -0.0325611918191314 -0.062762560254855 0.0600155324726122 -0.00745774679471391 0.0933225155629304 -0.0677605311147749 0.0310572199058558 0.000683735860166118 0.12114679354168 0.0273682604229063 -0.0404960035255129 0.100591415380188 0.0829323704379949 0.0671784619264675 0.00686127541624179 0.051411844803746 -0.0437212376649601 0.0235735210496245 0.0659541224550693 0.00525255992838871 0.0477855609641493 0.0223442937564653 0.00568785007493196 0.000266661405490322 -0.00275641820738351 0.0510668476915052 0.0461221570017992 -0.0233792013966787 -0.058375424067824 0.028221149304995 -0.0288838344190183 -0.0548217641902133 0.0482861285754476 -0.00905003890961012 0.0758062479048013 -0.0591438163935129 0.0255235904715697 -0.00177157151383935 0.0999838350490465 0.0205094679794906 -0.0366189810000271 0.0828882943136175 0.0671784619264675 0.0617631236862641 0.0117525348413641 0.052204844907584 -0.0171503022235395 0.0389573474528528 0.0590238933310336 0.00878991265227885 0.0567151411633483 0.0235629031940631 0.0228861970008722 0.0204338581827212 0.0175638907691266 0.0488084185981191 0.0442762011716884 -0.00378854597924713 -0.0283692181141537 0.0302654782479146 -0.0104702089864427 -0.0248966716877106 0.0466810959627405 0.0110656273479028 0.0685914607665231 -0.027120218119098 0.0211916254144342 0.0133713330985715 0.0803274379804908 0.0296379518653182 -0.00917003311669867 0.00950733225267566 0.0068612754162418 0.0117525348413641 0.00579142182426778 0.0131577952624963 0.0117856837819247 0.0186992929943493 0.0101776494529567 0.00425891652240739 0.0191382461181393 0.00645554570367515 0.0158846015441607 0.0170712243185868 0.0164659664176226 0.0105008008785478 0.00964745303468412 0.0108409370383402 0.011122725974723 0.00857947126307491 0.00851118207049477 0.0119175881943944 0.0103762938028744 0.0147645364323098 0.0123309897232221 0.012637278253383 0.00254721964630818 0.0123392438508897 0.00771259317015302 0.0126800068632322 0.0142513837172234 0.0643791627164946 0.051411844803746 0.052204844907584 0.0131577952624963 0.0470495989295207 -0.000848446856654554 0.0431637625556737 0.048933993283779 0.00977510640121653 0.0555071235024547 0.02170465453138 0.0298004625932581 0.0292269507348875 0.0267474900242421 0.0423553237778054 0.0385327158721362 0.00728294633092717 -0.00899639136739272 0.0281394754193564 0.000675530135516445 -0.00593964060131988 0.0408114070136169 0.0208332575559666 0.0573227081321525 -0.00678270029309243 0.0165651680688099 0.0201848087634951 0.0610289187169428 0.0314360420362163 0.00675579920859723 -0.0495366330834786 -0.0437212376649601 -0.0171503022235395 0.0117856837819247 -0.000848446856654542 0.0684667042561843 0.0369585765492405 -0.0208499000875407 0.00850745657253676 0.0195819943012646 0.00180434722178253 0.042451493410837 0.0501308897338612 0.0506774347370917 -0.00841686763851576 -0.00712001280886565 0.0499944363637104 0.0778123331454642 0.00353511081681727 0.047369724514395 0.0774157068988091 -0.00663966601277362 0.0505138338307351 -0.0220978958293409 0.0828707081324624 -0.0121714990607543 0.0377498500728268 -0.0543601035818623 0.0215728155312605 0.0702602734308179 0.032392779146998 0.0235735210496245 0.0389573474528528 0.0186992929943493 0.0431637625556737 0.0369585765492404 0.0604030683470199 0.0338845473007653 0.013755080171894 0.0622700690426726 0.0211225684139769 0.0510388148027409 0.054740584338676 0.0527425609781959 0.0346380841191454 0.0318081338588962 0.034315556853552 0.0345547724874134 0.0280440701852602 0.0267411689613347 0.0371707960738655 0.0341860941067182 0.0471677972758245 0.0409758186369918 0.0393963011045024 0.00865163794016675 0.0395297308317907 0.0266267684629125 0.0410452507251998 0.0449991707298244 0.0810689532034453 0.0659541224550693 0.0590238933310336 0.0101776494529567 0.048933993283779 -0.0208499000875407 0.0338845473007653 0.0567184290513842 0.00763354197835819 0.0517261445507159 0.0219334466663459 0.0184540258379041 0.0156204589198864 0.0128953066778725 0.0462841300237181 0.0419502336889737 -0.00704719427071437 -0.032007466161975 0.0280872723183638 -0.0131188527015599 -0.0287286711319365 0.0441680841014552 0.00682303533499611 0.0657630391629541 -0.0311923012482871 0.0206919472594538 0.00987531724699025 0.0790091712989869 0.0262368791468966 -0.0135042844209968 0.00723859743041877 0.00525255992838872 0.00878991265227885 0.00425891652240739 0.00977510640121653 0.00850745657253676 0.013755080171894 0.00763354197835819 0.00313250949992457 0.0141434060498184 0.00478794886709362 0.0116449573116017 0.0124986981604577 0.0120472235058898 0.00782894836697883 0.0071905305986783 0.00787206267385261 0.00798157028767676 0.00635914347893124 0.00615120842490258 0.0085733230374413 0.00773010501205235 0.0107841881246033 0.00923726604119257 0.00908825921105944 0.00193542975243093 0.00902874543056264 0.0059229761790014 0.00933984492253078 0.0103322557487092 0.0614055106488573 0.0477855609641493 0.0567151411633483 0.0191382461181393 0.0555071235024547 0.0195819943012646 0.0622700690426726 0.0517261445507159 0.0141434060498184 0.0716741328870241 0.0262664810407564 0.048083841820535 0.0497132786978242 0.0469390143282528 0.0476677801980033 0.0435272585332005 0.0236646513502061 0.0127353914422157 0.0344133334554462 0.0150444371570581 0.0162389282125934 0.0463723554557685 0.0398803900221919 0.0612930167970301 0.0168800391577657 0.0159728050077307 0.0352738026206232 0.0559844775340679 0.0437441958302761 0.0291337114122371
It isn't clear what you mean when you say that you want A * Ainv = 1 for a non-square matrix. Do you mean a matrix with all ones? Do you mean a non-square matrix in which the main diagonal is 1 and the rest is 0? What size do you expect A*Ainv to be?

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更多回答（1 个）

Nara Lee
Nara Lee 2021-4-24
assume that I have S11[121 1],S21 [121 1] ,S12[121 1],S22[121 1] ,and S=[S11 S12;S21 S22] So S would be S[242 2]
THEN I thought if for example S11*invS11=1 , S12*inv(S12)=0 , S21*inv(S21)=1, S22*inv(S22)=0 but in form of TINV=[242 2]

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