Function & Matrix Discussion
Function & Matrix Discussion
& a factor of m
     ⑪N                             factor of
                                                m
                                                    "
"his a
nRM
                                                             ⑪
                                                60            Symmx
                         =
                                                             70
                                                             -
                                                        30
                                                              [
                                                        -
BB-
     ⑮ ⑰
                                    W
9)              >
     *
        &#
     -
       ↑⑮
     (1 , 3)     231)
     -
       *
e
7
         =
              =>
                   flul
                        n
                             =
                             E+
                                         *
                                         log
                                         0
                                             2
                                             S
20
              E
                        n    > 0
l RF I
1092 T O
                                                 T
                     &
E       fin   =                              t    n+
                                                       G
1) -
              10
                         (n
                          l N
                                 -
T -
log , (1 -u) + 0
    M
          [     1-m >    0
                   n + 67,       0
I
)                   ⑪
                        ⑬
en((1 0))
                    #
                ,
(5 a)
 ,
  (0   ,
           8)
 -
 -
·
P                     M
                                      +2
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               asinu + blo 1
-
(+ 1[
=
                  since-un   =
                                  v
        -v        Gnu-com-
                  Flanu-ca)1        2
      -
          21
                  ECSinn-uul +3    15
        ↓
                                                  Sa
    logst     -
                    "((5-(            + 3)    =
                                                   O
                                                  logy5
                                              - 2
                                 f(u)
                      02
                  #          flue [0 2]   .   .
    B                                                Su+ 5           =
                                                                         (n
①
        f(ul
                   (UTH
                                                             ↑
                                         try
               =
             (u)
                       +o     +23
                             (E   -- th
         =
                   +                             +
                                         /
    =
                       (n)   +
                                     +1000243.
                                     Iro
                                                             12
                         [R]     +       Suz         =
                                                                           a
                                 f   :   - B
    fr                                   ↑
                             ((              y   =       n
                                                                 -
                                                                     (4)
                                                         ↑
9)   ful :
             J
                                                  #
 =
     1)   2- I       0   =>    (ul + 2   =
                                              C
                                              + 12
                                              r
2- I2)
                                 I
                                                  +
                         =
                               Foy
                     Ine
                     =
                     z
                               (-V
                     1                   v(8) Ve
+                 ~
                                    (r)
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                                              =   2
                                                  (1 F,
                                                          -
11]
⑳       O
                  "S
                  5
    E
    I
I
                   -
    -
                  4
                       -
[]C = 5
                                26
    -
                      and                 -
     &                      -
                            -
                       [
    A   03
        W
        W   n73
                            u
        -
                            -
                            **
                                         N75
        =
                                                          7
                                    51]
                            -
                      -IC           tred
EX3   I
                    i
-
-
          5
          24 34
                  -
            -
                  Fire
          -
[ logi, 70
Lu
                    G
                    (ty
                           ⑭
                   F
                         co
                                 ⑳
R =E (1)                    :   new          a      Any yt =
                                                   n 3uy     -
                                                                 ny + 3y
                                                                             ?       0
x(x -
                                                   E
                                                   ( (3y)                        =   o
                                                  C
                                                  R Y or
                                                  &
                                                    =
                                                         [R 3Y
                                                         27  9       >
                                                                         =
                                                                 /I aI
                                                  =>
                                                                     9
                                                                                 M
                                                                         54I
                                                  z                      M
-
 Ref :        URR                                                    1
 -            -
              -
symm
-
-
          :
               #ER
                                             No   symm
                  (1 , 3)   (R ?         -
                                             -
Trans !
-
                                (2   ,
                                             3) ER
-
(9 3), ER
                                (27      ,
                                             3) R = Panat                        -
⑰   fir                        R
      21th+gi                                    343--AP
                       &
                                   f(W   ,
                           ,
· 1 = +5
                       =
                                             -R
          Hm
                                   -
                                   2
                                             2
                                             +            =
                           it                                 R" domain
⑩   Re        :
                                     W
                                     w
                                     -
                                     -
                                     n
                                                      o
                                                      -
                                             n2   y
                                                          =
                                                              RAT Rand        -
                                   +,3                        0
                                                                  ,
                                                                      1
                                                                          ,
⑰
        (                                     -
2 , +])
·
                                         [
                                     &
                                                             /
                                                             4
        loge (U
                    -
                        34+ 2)   #   0   =>
                                              -
                                              22-3 +  n +2   1
             -
                                     -but     20
                                                  #
                  ~          -
Iv-5u + 611/29)
    =
        (v
         -
             -
                    s (10
                 ju +    -
                    Gr= -3) OE
⑯ P(s)          -
                    power set        S   =
                                              &112,       . . .       los
                                              2
                                                  ↓
                        past             RI                   PCS)        1
                J
                        -
                        -
7 I
· W
/ -
                        -
                                                                  &
                             C (AMBY VIDAY                            0           E
                                                                                  A B
                                                                                   =
                 B11                   B
                                                                  =
=           DR                                                                    =
                 ,              --
                             ↓
            z
                               L
                               -
        -
                                                          A                   B
                               G
                               ⑧
                                                          I
     b3 1 (a d)
 (49 -  ,
                U(2b 212443)
                    ,            ,
                                                          =
                                                                  &
            Ud                                        ⑳   ~   &
                                                                          I
                                                                          6
                                                      ⑧
    =
=>
     ·
     Sym                     -
                                 e
g        flut   =   C· esse
                    cosec
                    -
                                 X
                                                  -
                                                               Functa-Domain
           until
                                                           b
                    -
                                                          Funct Range
                                                       Actual
             E
                                                  Coech-Domain
          caseve
     Pareing
                                                                                 .
                             Paregcore
                             -
                             -
                                              -
                       A
                      Sinn       -    [+ , 13
                     EX
                                         -
                                                               #
         let va
                                         ,   of
     ~       # rentgen               I
                14370
                7
                -
                                 =
                                         -
                                                               I,
                                         -
=> UE(-N , -
                                                      1)   U   (1   ,   N)   -
                                                                                 I
*
                                                P
                     n   =
                              200 - 22              . . . .
                              -m
                                        -
                                     -
                                     1 22
                                        ,
                                                      I
(1)23 + 24(1) + -- -
                                     ⑮40
            1(23 + 24 +               m) + 2()-H                     )
                                 -
....
P   =
        [   ,   b)
                         =>
                             sec-tanb   =
                                            -
                                                13
                                Eb
                                 a=
                     ard
                     -
4)   f f(x)   -
+((u)
      Fi)
                              -
t (an + yu)
     *
                                  -
                                      -
 =
       (ii) In
                                  -
                  ty(l-rhinna)/ Du
                                      -
                   n          5
                                          ↑
                          -
                                  =       -
⑯D =                            152
- 1 <9-511
  -
  41946
                           42b6
          inO
                   ·
 a
                                  B
              T
  6
          -
              - ·
                & ·         ·
              ·
                       -
AcB
+ 2
=E
                                  -
⑱                n   -
                         2y   -
                                  2z    =    -x
                                             -
                 n + 24 + z
                                            Jy
                                    =
- n -
                         y    =    J7                C       non      trivial
                                                                      -
                                                                      -
                                                                                   .
                 [
                                                             27            0
                         2) J)x                  2y
                              -             -            -        =
    =
                                                 j)y + z                   0
                                                                               -
                                        (2
                                                                  =
                              n +
                                             -
                                                     Jz                0
                             - n    -
                                        y        -            =
                         I                                                 I
                                                                      2
    D=   0   =                I-d            -   2            -
                              I                      d
                                                                       I        =O
                                             2   -
                             -              -                 -
⑭                                  (A))
                                   -
                                          =   Id
Ladyladna)) =
                                   12t
          =
                               t
                          12
      I
           IAl8   =       12t
                           4/8
           1 Al   =
                      12           =
                                   12
                                   -
                                              253
                           IDTXIdl
    ↳ ladja)          =
                                          =
(M
                   /,                                       I
     =                     I
              +
          e                                           + c
                                    -
                                                      2C
                                            25
                                                  -
                  ⑳Rs
                   &   -
                               Ri R2
                                -
         -10       j
                                                       I
                  -
     =>           ets(nz       -
                                        +   rt)
                               -
              set
                ↳
                                    o
④   IAl = 2            ladTA)       =   1AI-1
        -
        =
                            20              n   =
                                                    ?
              /"
                           84   .
                       C
    -
                   =
        g) add                  o
                                                        -
                                 -
    =
              ⑭
                    GB               Sector   2
                                              -
--
A                        :
                             (ii)
                                                  X   =
A = XB
( I
    [ (-                                                  J
I
2X/
a tac =
                    t
                    >
                                              2
                                                          3
                                                                    (bibiy
                                                          ↓ -
           O
                                                            -
       =        [bi
                 -
                =>
                 -
                    + 5 (1 +kY & bibz (
                             -
                                 >
                                       *  E
                                        2k)           -
                                                          2+
                                                          -
                                                            S
                                 3
                                          ⑰
                                          W
2)     +   :    R-R                   ⑭
                     #
                             -            Sinn-un = r2
2 Lam -un) = 2
gr (m -
4) = 0
wa
                m        y
                                  =