Question

B=
Find the value of 3A-2B
यदि (If) A= 5 7
3 2
23
5 7
. मान ज्ञात कीजिए। ​

Answer 1

Answer:

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Step-by-step explanation:

Answer :

3.1 lexz voyksdu (Overview)3.1.1vkO;wg la[;kvksa (;k iQyuksa) dk ,d vk;rkdkj Øfer Øe foU;kl gSA mnkgj.kkFkZ,A = 434334xxxla[;kvksa (;k iQyuksa)vkO;wg osQ vo;o ;k izfof"B;k¡ dgrs gSaAvkO;wg osQ vo;oksa dh {kSfr”k js[kk,¡] vkO;wg dh iafDr;k¡ (Rows) rFkk mQèoZ js[kk,¡ vkO;wg osQLraHk (Columns) dgykrs gSaA3.1.2vkO;wg dh dksfV(Order of a matrix)miafDr;ksa rFkk nLraHkksa okys fdlh vkO;wg dks m × ndksfV (Order)  dk vkO;wg vFkok osQoym × nvkO;wg dgrs gSaAmi;qZDr mnkgj.k esa] A ,d 3 × 3 dksfV dk vkO;wg vFkkZr~ 3 × 3 vkO;wg gSAO;kid :i esa ,d m × nvkO;wg dk fuEufyf[kr vk;rkdkj Øe foU;kl gksrk gS%A = [aij]m × n  = 11121312122232123nnmmmmnmnaaaaaaaaaaaa×1≤i≤m, 1≤j≤nrFkki,  j∈N.vo;o aijog vo;o gS tks i oha iafDr vkSjj osa LraHk esa fLFkr gksrk gS rFkk blsA  dk (i, j)ok¡ vo;o dgrs gSaA m × nvkO;wg esa vo;oksa dh la[;k mngksrh gSAvè;k;3vkO;wg21/04/2018

3.1.3vkO;wg osQ izdkj (Types of Matrices)  (i),d vkO;wg] iafDr vkO;wg dgykrk gS ;fn mlesa osQoy ,d iafDr gksrh gSA (ii),d vkO;wg] LraHk vkO;wg dgykrk gS ;fn mlesa osQoy ,d LraHk gksrk gSA(iii),d vkO;wg ftlesa iafDr;ksa dh la[;k LraHkksa dh la[;k osQ leku gksrh gS] ,d oxZvkO;wg (Square matrix) dgykrk gSA vr% ,d m × nvkO;wg] oxZ vkO;wgdgykrk gS ;fn m = ngks vkSj mls ‘n’ dksfV dk oxZ vkO;wg dgrs gSaA(iv),d oxZ vkO;wg B = [bij]n×nfod.kZ vkO;wg (Diagonal matrix) dgykrk gS ;fnfod.kZ osQ vfrfjDr blosQ lHkh vU; vo;o 'kwU; gksrs gSa vFkkZr~ ,d vkO;wgB = [bij]n×nfod.kZ vkO;wg dgykrk gS ;fn bij = 0, tc i≠jgksA (v),d fod.kZ vkO;wg] vfn'k vkO;wg (Scalar matrix) dgykrk gS ;fn blosQ fod.kZosQ vo;o leku gksrs gSa] vFkkZr~ ,d oxZ vkO;wg B = [bij]n×nvfn'k vkO;wgdgykrk gS ;fnbij = 0, tc i≠j, bij = k, tci=j, tgk¡kdksbZ vpj gSA(vi),d oxZ vkO;wg ftlosQ fod.kZ osQ lHkh vo;o ,d gksrs gSa rFkk 'ks"k vU; lHkhvo;o 'kwU; gksrs gSa] rRled vkO;wg (Identity matrix) dgykrk gSAnwljs 'kCnksa esa] oxZ vkO;wg A = [aij]n×n ,d rRled vkO;wg gS ;fn aij = 1, tci = jgks rFkkaij = 0, tci≠jgksA           (vii),d vkO;wg] 'kwU; vkO;wg ;k fjDr vkO;wg dgykrk gS ;fn blosQ lHkh vo;o 'kwU;gksaA ge 'kwU; vkO;wg dks O }kjk fu:fir djrs gSaA          (viii)nks vkO;wg A = [aij] rFkk B = [bij] leku dgykrs gSa ;fn(a)  os leku dksfV osQ gksa] rFkk(b)  A dk izR;sd vo;o] B osQ laxr vo;o osQ leku gks] vFkkZr~] irFkk josQ lHkh ekuksa osQ fy, aij = bijgksA3.1.4vkO;wgksa dk ;ksx (Addition of matrices)nks vkO;wgksa dk ;ksx rHkh laHko gS tc os leku dksfV osQ gksaA3.1.5,d vkO;wg dk ,d vfn'k ls xq.ku (Multiplication of matrix by a scalar);fn A = [aij] m×n,d vkO;wg gS rFkk k,d vfn'k gS rks kA ,d ,slk vkO;wg gS ftlsA osQ izR;sdvo;o dks kls xq.kk djosQ izkIr fd;k tkrk gS] vFkkZr~] kA = [kaij]m×n42   iz'u iznf'kZdk21/04/2018