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लीनियर एलजेब्रा उदाहरण
55
चरण 1
सर्वसमिका मैट्रिक्स या आकार की इकाई मैट्रिक्स 55 5×55×5 वर्ग मैट्रिक्स है जिसमें मुख्य विकर्ण और शून्य कहीं और होते हैं.
[1000001000001000001000001]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
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⎥
⎥
⎥
⎥⎦
चरण 2
Multiply the scalar 55 by the identity matrix.
5[1000001000001000001000001]5⎡⎢
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⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
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⎥
⎥
⎥
⎥⎦
चरण 3
चरण 3.1
मैट्रिक्स के प्रत्येक अवयव से 55 को गुणा करें.
[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⎤⎥
⎥
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⎥
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⎥⎦
चरण 3.2
मैट्रिक्स में प्रत्येक तत्व को सरल करें.
चरण 3.2.1
55 को 11 से गुणा करें.
[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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.2
55 को 00 से गुणा करें.
[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⎤⎥
⎥
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⎥⎦
चरण 3.2.3
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
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⎥⎦
चरण 3.2.4
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
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⎥⎦
चरण 3.2.5
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.6
55 को 00 से गुणा करें.
[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⎤⎥
⎥
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चरण 3.2.7
55 को 11 से गुणा करें.
[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⎤⎥
⎥
⎥
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⎥⎦
चरण 3.2.8
55 को 00 से गुणा करें.
[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⎤⎥
⎥
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⎥⎦
चरण 3.2.9
55 को 00 से गुणा करें.
[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⎤⎥
⎥
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⎥⎦
चरण 3.2.10
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
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⎥⎦
चरण 3.2.11
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
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चरण 3.2.12
55 को 00 से गुणा करें.
[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⎤⎥
⎥
⎥
⎥
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⎥⎦
चरण 3.2.13
55 को 11 से गुणा करें.
[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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.14
55 को 00 से गुणा करें.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
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⎥⎦
चरण 3.2.15
55 को 00 से गुणा करें.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.16
55 को 00 से गुणा करें.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.17
55 को 00 से गुणा करें.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.18
55 को 00 से गुणा करें.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.19
55 को 11 से गुणा करें.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
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⎢
⎢
⎢⎣50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
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⎥
⎥
⎥⎦
चरण 3.2.20
55 को 00 से गुणा करें.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500000500000505⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
चरण 3.2.21
5 को 0 से गुणा करें.
[5000005000005000005005⋅05⋅05⋅05⋅1]
चरण 3.2.22
5 को 0 से गुणा करें.
[50000050000050000050005⋅05⋅05⋅1]
चरण 3.2.23
5 को 0 से गुणा करें.
[500000500000500000500005⋅05⋅1]
चरण 3.2.24
5 को 0 से गुणा करें.
[5000005000005000005000005⋅1]
चरण 3.2.25
5 को 1 से गुणा करें.
[5000005000005000005000005]
[5000005000005000005000005]
[5000005000005000005000005]