Determinants in Bangla

নির্ণায়ক পাওয়ার পয়েন্ট স্লাইড

1. A=   wbY©vqK(   D=det(A)=   ‡h wbqg Øviv cÖ‡Z¨KwU eM © g¨vwU ª‡·i GKwU gvb cvIqv hvq Zv‡K wbY©vqK e‡j |

2. wbY©vq‡Ki gvb wbY©qt GK µ‡ gi eM © g¨vwU ª· Gi wbY©vqK   ` yB µ‡ gi eM © g¨vwU ª· A= Gi wbY©vqK   [ mvwi Kjv‡gi Ae ¯’ vb Abyhvqx fzw³¸wj ‡ jLv |]

3. wbY©vq‡Ki gvbt wZb µ‡ gi eM © g¨vwU ª· A Gi wbY©vqK   D`vniY: Gi gvb wbY©q Ki| D:  

4. mvivR WvqvMÖv‡gi gva ¨‡g wbY©vq‡Ki gvb † ei Kiv hvq - A=   D`vniY: Gi gvb wbY©q Ki| D:  

5. wbY©vqK A=   fzw³ Gi Abyivwk fzw³ Gi Abyivwk fzw³ Gi Abyivwk fzw³ Gi Abyivwk fzw³ Gi Abyivwk fzw³ Gi Abyivwk BZ¨vw `   cÖ‡Z¨KwU fzw³i ¯^-¯^ mvwi - Kjvg eivei fzw³ ev ` † i‡L Aewkó fzw³i Øviv MwVZ wbY©vqKB Abyivwk | Abyivwk I mn¸YK

6. Abyivwk I mn¸YK - Zg fzw³i wPý Avi wPýhy³ Abyivwk‡K mn¸YK e‡j |   wbY©vq‡Ki fzw³ Gi mn¸YK Abyiƒcfv‡e mKj fzw³i mn¸YK † ei Kiv hvq |  

7. wbY©vqK A=   `ª óe ¨: 1. wbY©vq‡Ki gvb wbY ©‡q 1g mvwi e¨envi Kiv n‡q‡Q | 2. ‡h † Kvb mvwi / Kjvg e¨envi K‡i GB GKB gvb cv‡ev | mn¸Y‡Ki gva ¨‡g wbY©vq‡Ki gvb wbY©q

8. Abyivwk I mn¸YK µ‡ gi wbY©vq‡Ki fyw³¸wji mn¸Y‡Ki wPý wb¤œiƒct `ª óe¨t Avgiv mn¸Y‡Ki fzw³¸wji wPý wn‡m‡e ai‡Z cvwi | (K) † Kvb wbY©vq‡Ki GKwU mvwi ev Kjv‡gi fzw³¸wj‡K Zv ‡`i mn¸YK Øviv ¸ YK‡i † hvM Ki‡j wbY©vq‡Ki gvb cvIqv hvq | (L) † Kvb wbY©vq‡Ki GKwU mvwi ev Kjv‡gi fzw³¸wj‡K Ab ¨ mvwi ev Kjv‡gi fzw³i mn¸bK Øviv ¸ YK‡i † hvM Ki‡j wbY©vq‡Ki gvb k~b ¨ nq |  

9. (i) ‡ Kvb wbY©vq‡Ki GKwU mvwi / Kjv‡gi mKj fzw³ k~b ¨ n‡j wbY©vq‡Ki gvb k~b ¨ nq | D`vt D= BZ¨vw `| (ii) ‡ Kvb wbY©vq‡Ki mvwi‡K Kjv‡g Ges Kjvg‡K mvwi‡Z cwibZ Ki‡j Zvi gv‡bi cwieZ©b nq bv | D`vt   wbY©vq‡Ki ag © (Properties of determinants)

10. (iii) wbY©vq‡Ki ` ywU mvwi / Kjvg ci¯úi ¯’ vb wewbgq Ki‡j gvb cwieZ©b nq bv Z‡e wPý cwieZ©b nq | D`vt (iv) ‡ Kvb wbY©vq‡Ki ` yBwU mvwi ev Kjvg GKB n‡j Zvi gvb ïb ¨ nq | D`vt D=   wbY©vq‡Ki ag © (Properties of determinants)

11. (v) wbY©vq‡Ki GKwU mvwi ev Kjvg‡K † Kvb msL¨v Øviv ¸Y Ki‡j Zvi gvb‡K H msL¨v Øviv ¸Y Ki‡Z n‡e | D`vt (vi) ‡ Kvb wbY©vq‡Ki GKwU mvwi ev Kjvg Gi cÖ‡Z¨K fzw³‡K ` yBwU ev Z‡ZvwaK msL¨vi † hvMdjiƒ‡c cÖKvk Kiv † M‡j wbY©vqKwU‡KI ` yB ev Z‡ZvwaK wbY©vq‡Ki † hvMdjiƒ‡c cÖKvk Kiv hv‡e | D`vt   wbY©vq‡Ki ag ©

12. (vii) GKwU wbY©vq‡Ki GKwU mvwi ev Kjv‡gi fzw³¸wji mv‡_ H wbY©vq‡Ki Aci GK ev GKvwaK mvwi ev Kjv‡gi fzw³¸wji ¸ wYZK † hvM / we‡qvM Ki‡j wbY©vq‡Ki gvb AcwiewZ©Z _ v‡K | D`vt উদাঃ মান নির্ণয় করঃ ( মূলনিয়মে বা নির্ণায়কের ধর্ম ব্যবহার করে )   wbY©vq‡Ki ag © (Properties of determinants)

13. mvwii Bs‡iwR ms‡ÿ‡c Kjv‡gi Bs‡iwR ms‡ÿ‡c   1g mvwi ev 2q mvwi ev 3q mvwi ev   1g Kjvg ev 2q Kjvg ev 3q Kjvg ev   `ªóe¨t †Kv‡bv wbY©vq‡Ki mvwi I Kjvg Gi Kg© c×wZ ms‡ÿ‡c cÖKvk Kiv hvq| ‡ hgbt 1g mvwi †_‡K 2q mvwi we‡qvM K‡i 1g mvwi‡Z emv‡bv‡K ev Øviv Ges 1g, 2q I 3q Kjvg † hvM K‡i Z… Zxq Kjv‡g emv‡bv‡K Øviv cÖKvk Kiv nq |   jÿYxqt

14. wbY©v‡qi gvb wbY ©‡qi mvaviY Gj`wi`g / cÖwµqv wbY©vq‡Ki fzw³mg~‡ ni gvb hw ` msL¨vq _ v‡K Zvn‡j mvaviYZ mivmwi gvb wbY©q c×wZ e¨envi Kiv nq| wKš ‘ wbY©vq‡Ki fzw³mg~‡ ni gvb hw ` exRMvwYwZK ivwk nq Zvn‡j wb¤œwjwLZ avcmg~n AbymiY Kiv fv‡jv - avc 1: wbY©vq‡Ki ag© e¨envi K‡i mvwi ev Kjv‡gi gvbmg~n‡K † QvU Kivi † Póv Ki‡Z n‡e | avc 2: wbY©vq‡Ki mvwi ev Kjv‡g † Kvb mvaviY gvb _ vK‡j Zv Kgb wb‡Z n‡e | avc 3: †h † Kvb GKwU mvwi ev Kjv‡gi fzw³‡K GKB Ki‡Z n‡e | Gi Rb ¨ mvwii mv‡_ mvwi ( Kjv‡gi mv‡_ Kjvg ) † hvM ev we‡qvM Kiv hv‡e | avc 4: ‡h † Kvb mvwi ev Kjv‡gi ` yBwU fzw³‡K k~b ¨ Ki‡Z † Póv Ki‡Z n‡e | KviY k~‡ b¨i mv‡_ Zvi mn¸Y‡Ki ¸ Ydj k~b ¨ nq| avc 5: †h mvwi ev Kjvg G ` yBwU fzw³ k~b ¨ _ vK‡j † mB mvwi ev Kjvg Gi gva ¨‡g we¯Ívi Ki‡Z n‡e | avc 6: me©`v hvnv cÖgvY Ki‡Z ejv n‡”Q † mB w`‡K † Lqvj † i‡L wbY©vq‡Ki Acv‡ikb¸wj Pvwj‡q † h‡Z n‡e | mKj‡K ab¨ev `