Методические рекомендации по выполнению контрольных работ по математике. Кулиш Н.В - 12 стр.

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51)2(13
11
23
)1(
11
11
=⋅−−⋅=
−
⋅−=
+
A ;
()
51)2(13
11
23
)1(
21
12
−=⋅−−⋅−=
−
⋅−=
+
A ;
()
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)1(
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13
=⋅−⋅=⋅−=
+
A ;
()
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)1(
12
21
−=⋅−−⋅−=
−
−=
+
A ;
31)1(12
11
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)1(
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=⋅−−⋅=
−
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+
A ;
()
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+
A ;
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A ;
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)1(
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=⋅−⋅=⋅−=
+
A .
Получаем
−
−
−
=
−
310
135
125
5
1
1
A . Тогда
=
=
⋅+⋅−+⋅
⋅+⋅+⋅−
⋅
+
⋅
−
+
⋅
=
⋅
−
−
−
=
2
1
3
10
5
15
5
1
638)1(50
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618)2(55
5
1
6
8
5
310
135
125
5
1
X .
Ответ: х = 3; y = 1; z = 2.
Задача 2.
12
                        3 −2
     A11 = (−1)1+1 ⋅         = 3 ⋅ 1 − ( −2 ) ⋅ 1 = 5 ;
                        1 1

                         3 −2
     A12 = (−1)1+ 2 ⋅         = −(3 ⋅ 1 − (−2) ⋅ 1) = −5 ;
                         1 1

                         3 3
     A13 = (−1)1+3 ⋅         = (3 ⋅ 1 − 3 ⋅ 1) = 0 ;
                         1 1

                       1 −1
     A21 = (−1) 2+1         = −(1 ⋅1 − (−1) ⋅1) = −2 ;
                       1 1

                         2 −1
     A22 = (−1) 2+ 2 ⋅        = 2 ⋅ 1 − (−1) ⋅ 1 = 3 ;
                         1 1

                         2 1
     A23 = (−1) 2+3 ⋅        = −(2 ⋅ 1 − 1 ⋅ 1) = −1 ;
                         1 1

                         1 −1
     A31 = (−1) 3+1 ⋅         = 1 ⋅ (−2) − (−1) ⋅ 3 = 1;
                         3 −2

                         2 −1
     A32 = (−1) 3+ 2 ⋅        = −(2 ⋅ (−2) − (−1) ⋅ 3) = 1;
                         3 −2

                         2 1
     A33 = (−1) 3+3 ⋅        = 2 ⋅ 3 − 1⋅ 3 = 3.
                         3 3

                   5 − 2 1
                 1    −1   
     Получаем A =  − 5 3 1  . Тогда
                 5         
                   0 − 1 3

          5 − 2 1  5        5 ⋅ 5 + (−2) ⋅ 8 + 1 ⋅ 6    15   3 
        1              1                              1   
     X =  − 5 3 1 ⋅  8  =  − 5 ⋅ 5 + 3 ⋅ 8 + 1 ⋅ 6  =  5  =  1  .
        5             6  5  0 ⋅ 5 + (−1) ⋅ 8 + 3 ⋅ 6  5 10   2 
           0  − 1 3                                        

     Ответ: х = 3; y = 1; z = 2.
     Задача 2.


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