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Линейная алгебра Примеры
55
Этап 1
Единичная матрица размера 55 представляет собой квадратную матрицу 5×55×5 с единицами на главной диагонали и нулями на остальных местах.
[1000001000001000001000001]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 2
Multiply the scalar 55 by the identity matrix.
5[1000001000001000001000001]5⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3
Этап 3.1
Умножим 55 на каждый элемент матрицы.
[5⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2
Упростим каждый элемент матрицы.
Этап 3.2.1
Умножим 55 на 11.
[55⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣55⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.2
Умножим 55 на 00.
[505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.3
Умножим 55 на 00.
[5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.4
Умножим 55 на 00.
[50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.5
Умножим 55 на 00.
[500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.6
Умножим 55 на 00.
[5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.7
Умножим 55 на 11.
[50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.8
Умножим 55 на 00.
[500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.9
Умножим 55 на 00.
[5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.10
Умножим 55 на 00.
[50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.11
Умножим 55 на 00.
[500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.12
Умножим 55 на 00.
[5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.13
Умножим 55 на 11.
[50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.14
Умножим 55 на 00.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.15
Умножим 55 на 00.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.16
Умножим 55 на 00.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.17
Умножим 55 на 00.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.18
Умножим 55 на 00.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.19
Умножим 55 на 11.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.20
Умножим 55 на 00.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000500000505⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.21
Умножим 55 на 00.
[5000005000005000005005⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005005⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.22
Умножим 55 на 00.
[50000050000050000050005⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050000050000050005⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.23
Умножим 55 на 00.
[500000500000500000500005⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000500000500005⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.24
Умножим 55 на 00.
[5000005000005000005000005⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005000005⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Этап 3.2.25
Умножим 55 на 11.
[5000005000005000005000005]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005000005⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
[5000005000005000005000005]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005000005⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
[5000005000005000005000005]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005000005⎤⎥
⎥
⎥
⎥
⎥
⎥⎦