Class notes 12 maths

jpU.g.kJR+jd; nul;b, ,.M.g
khtl;l Ml;rpah;
rptfq;if khtl;lk;




jpU.,uh.Rthkpehjd;
Kjd;ikf;fy;tp mYtyh;
rptfq;if khtl;lk;




gs;spf;fy;tpj;Jiw
jpU.nr.rz;Kfehjd; jpU.[p.Kj;Jrhkp
khtl;lf;fy;tp mYtyh; khtl;lf;fy;tp mYtyh; k
NjtNfhl;il rptfq;if

rptfq;if khtl;lk;
xUq;fpizg;ghsh;
jpUkjp.[h.gpugh
jiyik Mrphpah;
muR Nky;epiyg;gs;sp
jkuhf;fp
rpwg;G topfhl;b
Mrphpah; FO


jpU.mU.Kj;Juhkd; jpU.R.
v];.tp.Nf. Nky;epiyg;gs;sp KUfg;g
tFg;G - 12 M.njf;$h;
jpU.nr.uh[P]; fz;zd; jpU.nk
muR Nky;epiyg;gs;sp muR khj
ghfNdhp
jpU.r.tpNdhj;Fkhh; jpU
muR Nky;epiyg;gs;sp muR
khq;Fb.
fzpjk;

, 1.APPLICATIONS OF MATRICES AND DETERMINANTS
2 MARK QUESTIONS 5. [ ]

1. [ ]
√| |

( ) ( ) | | ( ) ( )( ) ( )
√| | √
. / [ ] [ ] [ ]
[ ]
√| |
2. 0 1
| | 6. [ ]
0 1
[ ]. . ( )
( ) 0 1
| |

3. [ ]
| | | | | |

| | | | ( ) ( ) ( ) ( )


| | .
[ ] [ ]
( )

[ ] 7. [ ]
| |

4. [ ] [ ] [ ] [

.

[ ] ( )
3 MARK QUESTIONS
[ ] [ ] [ ] 1. 0 1 ( ) ( ) |
| |

,| | 0 1 0 1 ( ) | | 0 1 0
| |
0 1 ( ) 0 1 ( )
( ) 0 10 1 0 1 ( ) ( ) ( )( ) ( )

( ) 0 10 1 0 1 ( ) 5. [ ]
( )( ) ( ) ( ) ( ) | |
[ ] [ ]
2. [ ]

( ) [ ]
√| |

| | ( ) ( )( ) ( )
√| | √ [ ]


( ) [ ] [ ]
( )
6.
( ) [ ] [ ] 0 10 1 0 1
√| |
| | 0 1
3.Prove that 0 1 is orthogonal
0 1 0 1
| |
0 1 0 1 0 1 0 10 1 0 1 0 1

0 10 1 0 1 ( ) ( ) ( )

0 10 1 0 1 ( ) A man is appointed in a job with a monthly salary of certain am
( ( ) ( ) annual increment. If his salary was Rs.19,800 per month at the e
years of service and Rs.23,400 per month at the end of the first m
4. ( ) ( ) 0 1.
find his starting salary and his annual increment. (Use matrix in
0 1 | | ( ) 0 1 problem.) Hint:
7.
( ) ( ) 0 1 ( )
| |

, | |
| | [ ] [ ] ( )
| |

| | [


( ) [ ][ ] [ ] ( )
( ) . /
( ) [ ][ ] [ ] ( )
In a competitive examination, one mark is awarded for every correct answer while ⁄ mark is
( )( ) ( ) ( ) ( ) | |
deducted for every wrong answer. A student answered questions and got marks. How
3. 0 1 0 1 ( )
many questions did he answer correctly? (Use Cramer’s rule to solve the problem).
Hint: ; ( ) 0 10 1 0 1 0 1
5 MARK QUESTIONS
| | ; ( ) 0 1
1. ( ) [ ] , ( )- ( )
( ) ( ) 0 1 ( )
| |
( ) ( )
( ) | | ; 0 1 ;
( ) [ ] [ ] ( )( ) | |
( )
( ) ( )
| | ; 0 1
| ( )| | | ( ) ( )
0 1 0 1
| |
0 10 1 0 1
( ) [ ] [ ] ( ) ( )( )
4. Solve the following system of linear equations by matrix inversio
, ( )- ( ) , ( )- [ ] ( )
| ( )|
( ) ( ) , ( )- ( ) [ ]6 7 [ ]

2. [ ] ( ) ( ) | | | | ( ) ( ) ( )

| | ( ) ( )( ) ( )