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12th MATHAMATICS NOTES
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+2கணிதயினல்
கற்ல் கட்டகம்
ள்ிக் கல்யித்துற
யிழுப்புபம் நாயட்டம்
(2021-2022)
திருநதி.K.கிருஷ்ணப்ிரினா
B.Sc.,M.A.,B.Ed.,
Kjd;ikf; fy;tp mYtyh;
யிழுப்புபம்.
, 1
gs;spf;fy;tpj;Jiw
tpOg;Guk; khtl;lk;
Nky;epiy ,uz;lhk; Mz;L
fzpjtpay;
கற்ல் கட்டகம்
2021-2022
திருநதி.K.கிருஷ்ணப்ிரினா
B.Sc.,M.A.,B.Ed.,
Kjd;ikf; fy;tp mYtyh;
tpOg;Guk;;
, 2
+2 fzpj ghlj;jpy; nky;y fw;Fk; khzth;fs; vspa Kiwapy;
Njh;r;rpngw rpwg;G gapw;rp ifNaL
khzth;fspd; ftdj;jpw;F
khzth;fs;fzpjj;jpy; 100 rjtPjk; Njh;r;rp ngWk; tifapy; ,r;rpwg;G gapw;rp
ifNaL jahhpf;fg;gl;Ls;sJ.
Blue Print ,y;yhj fhuzj;jpdhy;midj;J mj;jpahaq;fisAk; ftdKld;
gbf;f Ntz;Lk;
,g;gapw;rp ifNal;by; cs;s 5 kjpg;ngz; tpdhf;fSf;fhd tpilfis ed;whf
gapw;rp Nkw;nfhz;lhy; 35/35 kjpg;ngz;fs; vspjhf nghJj;Njh;tpy; ngwyhk;.
ghlg; Gj;jfj;jpy; xt;nthU mj;jpahj;jpYk; ,Wjp gapw;rpapy; cs;s xU
kjpg;ngz; tpdhf;fs; nkhj;jk; 250f;Fk; jPtpu gapw;rp Nkw;nfhz;lhy; 10 Kjy;
15 tiu kjpg;ngz;fs; fz;bg;ghf ngw;W tplyhk;.
Njitahd,lq;fspy; glq;fs; tiua Ntz;Lk;> glj;jpw;F kjpg;ngz;fs;
cz;L.
xt;nthW tpilf;Fk; jPh;T fhz cjTk; #j;jpuj;ij mtrpak; vOj Ntz;Lk;.
Njh;T neUq;Fk;NghJ mtru mtrukhf fzf;Ffis kdg;ghlk; nra;tij
jtph;j;J Muk;gk; KjNy Ghpe;J fzf;Ffis nra;J ghh;j;jy; Ntz;Lk;.
Njh;T vOJk;NghJ vt;tpj Fog;gKk; ,y;yhky; vOJtJ mtrpak;.
Nfs;tp vz;izAk;> Nfs;tpapy; cs;s tptuq;fisAk; ,U Kiw rhp ghh;f;f
Ntz;Lk;.
jkpo;ehL khepy ngw;Nwhh; Mrphpah; fofk;(PTA) ntspapl;Ls;s 6 khjphp
tpdhj;jhs;fSf;F gapw;rp Nkw;nfhz;L Njh;T vOjp gofpdhy; $Ljy;
kjpg;ngz; ngWtJ cWjp.
khzth;fs; vy;yh tpdhf;fSf;Fk; KOikahd gjpy; njhpatpy;iy vd;why;
$l tpilj; njhpe;j mstpw;F gjpy; mspj;jhy; chpa epiy kjpg;ngz;fis
(Step Mark)vspjhfg; ngw;W tplyhk;.
vdNt ek;gpf;ifNahL Njh;T vOJq;fs; 100 rjtPj Njh;r;rp ngw;W
khtl;lj;jpw;Fk; kw;Wk; khepyj;jpw;Fk; ngWik Nrh;j;jpl tho;j;Jf;fs;.
,td;
+2 fzpjtpay; rpwg;G gapw;rp ifNaL njhFg;ghsh; FO
Kidth; K. jpUKUfd;
muR Nky;epiyg; gs;sp> tOjht+h;
jpU.B. rPdpthrd;
jpU.E. ,uhN[\;Fkhh;>
muR Mjpjpuhtplh; ey Nky;epiyg;
muR Nky;epiyg; gs;sp> rhuk; gs;sp>ftiu
jpU. S. ehfKj;J ; jpU. G.K.gh];fud;
muR Nky;epiyg; gs;sp> gpy;Y}h; muR Nky;epiyg; gs;sp> Jk;g+h;
jpU.P.; KUfd;
jpU. K. NjNte;jpud;
muR Nky;epiyg; gs;sp> fhiz muRநாதிரி பண்கள்Nky;epiyg; gs;sp>
tpOg;Guk;;
, 3
1.mzpfSk; mzpf;Nfhitfspd; gad;ghLfSk;
(Important 2 & 3 Marks)
𝟖 −𝟒 𝟏 𝟑
𝟏) 𝑨 = vd;w mzpapd; 𝟐) 𝑨 = vd;w mzpapd;
−𝟓 𝟑 𝟐 −𝟓
𝑨 (𝒂𝒅𝒋𝑨) = (𝒂𝒅𝒋𝑨) 𝑨 = 𝐀𝐈2 vd;gijr; 𝑨 (𝒂𝒅𝒋𝑨) = (𝒂𝒅𝒋𝑨) 𝑨 = 𝐀𝐈2 vd;gijr;
rupghu;. (3-Marks) rupghu;. (3-Marks)
jPh;T: jPh;T:
𝟖 −𝟒 𝟑 𝟒 𝟏 𝟑 −𝟓 −𝟑
𝐀= , adj A = 𝐀= , adj A =
−𝟓 𝟑 𝟓 𝟖 𝟐 −𝟓 −𝟐 𝟏
𝟑 −𝟒 𝟏 𝟑
𝑨 = = 𝟐𝟒 − 𝟐𝟎 = 𝟒 𝑨 = = −𝟓 − 𝟔 = −𝟏𝟏
−𝟓 𝟖 𝟐 −𝟓
𝟖 −𝟒 𝟑 𝟒 𝟏𝟑 −𝟓 −𝟑
𝐀 𝒂𝒅𝒋 𝑨 = 𝐀 𝒂𝒅𝒋 𝑨 =
−𝟓 𝟑 𝟓 𝟖 𝟐
−𝟓 −𝟐 𝟏
𝟒 𝟎 −𝟏𝟏 𝟎
= = 𝐀𝐈 = = 𝐀𝐈
𝟎 𝟒 𝟎 −𝟏𝟏
𝟑 𝟒 𝟖 −𝟒 −𝟓 −𝟑 𝟏 𝟑
𝒂𝒅𝒋 𝑨 𝑨 = 𝒂𝒅𝒋 𝑨 𝑨 =
𝟓 𝟖 −𝟓 𝟑 −𝟐 𝟏 𝟐 −𝟓
𝟒 𝟎 −𝟏𝟏 𝟎
= = 𝐀𝐈 = = 𝐀𝐈
𝟎 𝟒 𝟎 −𝟏𝟏
vdNt 𝐀 (𝐚𝐝𝐣 𝐀) = (𝐚𝐝𝐣 𝐀) 𝐀 = 𝐀𝐈 vdNt 𝐀 (𝐚𝐝𝐣 𝐀) = (𝐚𝐝𝐣 𝐀) 𝐀 = 𝐀𝐈
𝟐 𝟑 𝟏 −𝟖 𝟏 𝟒
𝟏
𝟑) 𝑨 = 𝟑 𝟒 𝟏 - ,d; Nru;g;G mzp 4)𝑨 = 𝟗 𝟒 𝟒 𝟕 vdpy;
𝟑 𝟕 𝟐 𝟏 −𝟖 𝟒
fhz;f. (2-Marks) 𝑨−𝟏 = 𝑨𝑻 ிறுவுக.(3-Marks)
jPh;T: jPh;T:𝑨−𝟏 = 𝑨𝑻
𝟏 −𝟑 𝟗 𝑨𝑨−𝟏 = 𝑨𝑨𝑻
𝑨𝑪 = 𝟏 𝟏 −𝟓 𝑻
𝑨𝑨 = I vd epWtpdhy; NghJk;.
−𝟏 𝟏 −𝟏
𝑨𝟐
𝟏 𝟏 −𝟏 −𝟖 𝟏 𝟒 −𝟖 𝟒 𝟏
𝟏 𝟏
𝒂𝒅𝒋 𝑨 = −𝟑 𝟏 𝟏 =𝟗 𝟒 𝟒 𝟕 𝟗 𝟏 𝟒 −𝟖
𝟗 −𝟓 −𝟏 𝟏 −𝟖 𝟒 𝟒 𝟕 𝟒
𝟖𝟏 𝟎 𝟎 𝟏 𝟎 𝟎
𝟏
=𝟖𝟏 𝟎 𝟖𝟏 𝟎 = 𝟎 𝟏 𝟎
𝟎 𝟎 𝟖𝟏 𝟎 𝟎 𝟏
𝑨𝑨𝑻 = I
𝟎 −𝟐 𝟎 −𝟏 𝟐 𝟐
5)adj (A)= 𝟔 𝟐 −𝟔 எில் 𝑨−𝟏 ஐக் 6)adj (A)= 𝟏 𝟏 𝟐 எில் 𝑨−𝟏 ஐக்
−𝟑 𝟎 𝟔 𝟐 𝟐 𝟏
காண்க.(2-Marks) காண்க.(2-Marks)
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