Математик-1 lecthure-1

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    y 101 -I

    y

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    ,

    y

    y

    y y

    y ,

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    y m n

    mn mn

    .

    !

    mnmm

    n

    n

    mxn

    aaa

    aaa

    aaa

    A

    .

    .

    .

    21

    22221

    11211

    ....

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    y

    .

    y i- j-

    .

    y

    . (m=n)

    y

    . (mn)

    ija

    ij

    a

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    y :

    !

    08

    31

    22xA

    333231

    232221

    131211

    33

    aaa

    aaa

    aaa

    Ax

    011

    !x

    A

    !

    c

    aAx

    2

    13

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    y

    .

    y .

    y

    0 .

    nnaaa ,.....,,

    2211

    1121 ,.....,, nnnaaa

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    :

    ! 50

    01

    22xA

    33

    22

    11

    33

    a

    a

    a

    A x

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    y .

    y d=1 .

    y ()

    () .

    daaann

    !,.....,, 2211

    !

    100

    010

    001

    33xA

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    y 0 0

    .

    y mx1, 1xn .

    0131x

    A

    !

    c

    aAx

    2

    13

    !

    00

    0022xA

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    y

    y y

    y

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    y

    .

    yC=A+B

    :ijijij bac ! mmni ,1,,1 !!

    !

    41

    76

    19

    35

    38

    41

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    y

    .

    !

    !

    mnmm

    n

    n

    mnmm

    n

    n

    aaa

    aaa

    aaa

    aaa

    aaa

    aaa

    A

    PPP

    PPP

    PPP

    PP

    .

    .

    .

    .

    .

    .

    21

    22221

    11211

    21

    22221

    11211

    ........

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    yA+B=B+A

    y(A+B)+C=A+(B+C)

    y(QP)A=Q(PA)

    yP(A+B)=PA+PB

    y(Q+P)A=QA+PA

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    y

    .y .

    y i-

    j- .

    mxrkxrmxkCBA !

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    !

    !

    nknn

    k

    k

    n

    n

    n

    bbb

    bbb

    bbb

    aaa

    aaa

    aaa

    A

    .

    .

    .

    .

    .

    .

    21

    22221

    11211

    21

    22221

    11211

    ....B

    ....

    njinjijijiij abababaC ! ....332211

    !

    !

    !

    !

    1336

    512

    143304130423

    123102110221

    100

    312

    B43

    21

    BA

    A

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    ABBA {.1

    B)(ABA)(5.

    AEEA4.

    CABAC)(BA3.

    C)(BAC)(BA.2

    !

    !

    !!

    PP

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    n

    nAAAA ! ....

    .

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    y

    . .

    !

    !

    50

    8641

    584

    061

    TA

    A

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    TT

    TTT

    TTT

    TT

    kAAk

    BABA

    BABA

    AA

    !!

    !

    !

    )(

    )(

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