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Confidence | Program | Detection | Match Type | Support
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100%
| dexvert
| LaTeX Document (document/latex)
| magic
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1%
| dexvert
| Text File (text/txt)
| fallback
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| file
| LaTeX document text
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99%
| file
| LaTeX document, ASCII text, with CR line terminators
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100%
| checkBytes
| Printable ASCII
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| perlTextCheck
| Likely Text (Perl)
| default
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100%
| siegfried
| fmt/281 LaTeX (Subdocument)
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100%
| detectItEasy
| Format: plain text[CR]
| default (weak)
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key | value |
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macFileType | [TEXT] |
macFileCreator | [ttxt] |
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 5c 73 65 63 74 69 6f 6e | 7b 62 61 63 6b 73 75 62 |\section|{backsub|
|00000010| 20 2d 2d 2d 20 73 6f 6c | 75 74 69 6f 6e 20 6f 66 | --- sol|ution of|
|00000020| 20 6c 69 6e 65 61 72 20 | 65 71 75 61 74 69 6f 6e | linear |equation|
|00000030| 73 7d 0d 5c 6c 61 62 65 | 6c 7b 66 6e 3a 62 61 63 |s}.\labe|l{fn:bac|
|00000040| 6b 73 75 62 7d 0d 5c 69 | 6e 64 65 78 7b 62 61 63 |ksub}.\i|ndex{bac|
|00000050| 6b 73 75 62 28 29 7d 0d | 5c 69 6e 64 65 78 7b 6c |ksub()}.|\index{l|
|00000060| 69 6e 65 61 72 20 65 71 | 75 61 74 69 6f 6e 20 73 |inear eq|uation s|
|00000070| 6f 6c 76 65 72 7d 0d 5c | 69 6e 64 65 78 7b 73 6f |olver}.\|index{so|
|00000080| 6c 75 74 69 6f 6e 20 6f | 66 20 6c 69 6e 65 61 72 |lution o|f linear|
|00000090| 20 65 71 75 61 74 69 6f | 6e 73 7d 0d 5c 62 65 67 | equatio|ns}.\beg|
|000000a0| 69 6e 7b 72 61 69 6c 7d | 0d 62 61 63 6b 73 75 62 |in{rail}|.backsub|
|000000b0| 20 3a 20 27 62 61 63 6b | 73 75 62 27 20 27 28 27 | : 'back|sub' '('|
|000000c0| 20 4c 69 73 74 20 27 2c | 27 20 4d 61 74 72 69 78 | List ',|' Matrix|
|000000d0| 20 27 29 27 20 3b 0d 5c | 65 6e 64 7b 72 61 69 6c | ')' ;.\|end{rail|
|000000e0| 7d 0d 0d 0d 54 68 65 20 | 5c 76 65 72 62 2b 62 61 |}...The |\verb+ba|
|000000f0| 63 6b 73 75 62 2b 20 66 | 75 6e 63 74 69 6f 6e 20 |cksub+ f|unction |
|00000100| 63 6f 6d 70 75 74 65 73 | 20 74 68 65 20 73 6f 6c |computes| the sol|
|00000110| 75 74 69 6f 6e 20 74 6f | 20 74 68 65 20 73 65 74 |ution to| the set|
|00000120| 20 6f 66 0d 6c 69 6e 65 | 61 72 20 65 71 75 61 74 | of.line|ar equat|
|00000130| 69 6f 6e 73 20 64 65 73 | 63 72 69 62 65 64 20 62 |ions des|cribed b|
|00000140| 79 3a 0d 0d 5c 5b 20 41 | 20 20 58 20 3d 20 42 20 |y:..\[ A| X = B |
|00000150| 5c 5d 0d 0d 54 68 65 20 | 6c 69 73 74 20 61 72 67 |\]..The |list arg|
|00000160| 75 6d 65 6e 74 20 74 6f | 20 5c 76 65 72 62 2b 62 |ument to| \verb+b|
|00000170| 61 63 6b 73 75 62 2b 20 | 69 73 20 74 68 65 20 72 |acksub+ |is the r|
|00000180| 65 73 75 6c 74 20 66 72 | 6f 6d 0d 5c 76 65 72 62 |esult fr|om.\verb|
|00000190| 2b 66 61 63 74 6f 72 28 | 41 29 2b 2e 20 54 68 65 |+factor(|A)+. The|
|000001a0| 20 73 65 63 6f 6e 64 20 | 61 72 67 75 6d 65 6e 74 | second |argument|
|000001b0| 20 74 6f 20 5c 76 65 72 | 62 2b 62 61 63 6b 73 75 | to \ver|b+backsu|
|000001c0| 62 2b 20 69 73 0d 74 68 | 65 20 6d 61 74 72 69 78 |b+ is.th|e matrix|
|000001d0| 20 24 42 24 2c 20 77 68 | 65 72 65 20 65 61 63 68 | $B$, wh|ere each|
|000001e0| 20 63 6f 6c 75 6d 6e 20 | 6f 66 20 42 20 69 73 20 | column |of B is |
|000001f0| 61 20 73 65 70 65 72 61 | 74 65 20 72 69 67 68 74 |a sepera|te right|
|00000200| 20 68 61 6e 64 20 73 69 | 64 65 2e 0d 0d 5c 76 65 | hand si|de...\ve|
|00000210| 72 62 2b 62 61 63 6b 73 | 75 62 2b 20 72 65 74 75 |rb+backs|ub+ retu|
|00000220| 72 6e 73 20 24 58 24 2c | 20 74 68 65 20 73 6f 6c |rns $X$,| the sol|
|00000230| 75 74 69 6f 6e 20 6f 66 | 20 74 68 65 20 6c 69 6e |ution of| the lin|
|00000240| 65 61 72 20 65 71 75 61 | 74 69 6f 6e 73 2e 20 45 |ear equa|tions. E|
|00000250| 61 63 68 0d 63 6f 6c 75 | 6d 6e 20 6f 66 20 24 58 |ach.colu|mn of $X|
|00000260| 24 20 63 6f 72 72 65 73 | 70 6f 6e 64 73 20 74 6f |$ corres|ponds to|
|00000270| 20 74 68 61 74 20 63 6f | 6c 75 6d 6e 20 6f 66 20 | that co|lumn of |
|00000280| 24 42 24 2e 0d 0d 0d 5c | 70 61 72 61 67 72 61 70 |$B$....\|paragrap|
|00000290| 68 7b 45 78 61 6d 70 6c | 65 7d 0d 5c 69 6e 64 65 |h{Exampl|e}.\inde|
|000002a0| 78 7b 65 78 61 6d 70 6c | 65 20 6f 66 20 62 61 63 |x{exampl|e of bac|
|000002b0| 6b 73 75 62 28 29 7d 0d | 5c 69 6e 64 65 78 7b 62 |ksub()}.|\index{b|
|000002c0| 61 63 6b 73 75 62 28 29 | 21 65 78 61 6d 70 6c 65 |acksub()|!example|
|000002d0| 7d 0d 5c 62 65 67 69 6e | 7b 76 65 72 62 61 74 69 |}.\begin|{verbati|
|000002e0| 6d 7d 0d 3e 20 41 20 3d | 20 72 61 6e 64 28 34 2c |m}.> A =| rand(4,|
|000002f0| 34 29 0d 20 41 20 3d 0d | 20 20 20 20 30 2e 34 39 |4). A =.| 0.49|
|00000300| 33 20 20 20 20 20 20 30 | 2e 31 36 31 20 20 20 20 |3 0|.161 |
|00000310| 20 20 30 2e 31 33 37 20 | 20 20 20 20 20 30 2e 38 | 0.137 | 0.8|
|00000320| 37 39 20 20 0d 20 20 20 | 20 30 2e 37 38 32 20 20 |79 . | 0.782 |
|00000330| 20 20 20 30 2e 30 36 34 | 32 20 20 20 20 20 20 30 | 0.064|2 0|
|00000340| 2e 34 34 36 20 20 20 20 | 20 20 30 2e 37 36 31 20 |.446 | 0.761 |
|00000350| 20 0d 20 20 20 20 30 2e | 35 39 31 20 20 20 20 20 | . 0.|591 |
|00000360| 20 30 2e 32 37 31 20 20 | 20 20 20 20 30 2e 33 36 | 0.271 | 0.36|
|00000370| 37 20 20 20 20 20 20 30 | 2e 38 35 32 20 20 0d 20 |7 0|.852 . |
|00000380| 20 20 30 2e 30 37 32 31 | 20 20 20 20 20 30 2e 30 | 0.0721| 0.0|
|00000390| 33 38 34 20 20 20 20 20 | 20 30 2e 39 34 39 20 20 |384 | 0.949 |
|000003a0| 20 20 20 20 30 2e 31 30 | 37 20 20 0d 3e 20 58 31 | 0.10|7 .> X1|
|000003b0| 20 3d 20 72 61 6e 64 28 | 34 2c 31 29 0d 20 58 31 | = rand(|4,1). X1|
|000003c0| 20 3d 0d 20 20 20 20 30 | 2e 38 31 32 20 20 0d 20 | =. 0|.812 . |
|000003d0| 20 20 20 30 2e 35 34 33 | 20 20 0d 20 20 20 20 30 | 0.543| . 0|
|000003e0| 2e 32 35 34 20 20 0d 20 | 20 20 30 2e 30 38 32 35 |.254 . | 0.0825|
|000003f0| 20 20 0d 3e 20 42 31 20 | 3d 20 41 2a 58 31 0d 20 | .> B1 |= A*X1. |
|00000400| 42 31 20 3d 0d 20 20 20 | 20 30 2e 35 39 35 20 20 |B1 =. | 0.595 |
|00000410| 0d 20 20 20 20 30 2e 38 | 34 36 20 20 0d 20 20 20 |. 0.8|46 . |
|00000420| 20 30 2e 37 39 31 20 20 | 0d 20 20 20 20 30 2e 33 | 0.791 |. 0.3|
|00000430| 32 39 20 20 0d 3e 20 58 | 32 20 3d 20 72 61 6e 64 |29 .> X|2 = rand|
|00000440| 28 34 2c 31 29 0d 20 58 | 32 20 3d 0d 20 20 20 20 |(4,1). X|2 =. |
|00000450| 30 2e 36 39 37 20 20 0d | 20 20 20 20 30 2e 31 33 |0.697 .| 0.13|
|00000460| 37 20 20 0d 20 20 20 20 | 30 2e 38 31 35 20 20 0d |7 . |0.815 .|
|00000470| 20 20 20 20 30 2e 39 37 | 34 20 20 0d 3e 20 42 32 | 0.97|4 .> B2|
|00000480| 20 3d 20 41 2a 58 32 0d | 20 42 32 20 3d 0d 20 20 | = A*X2.| B2 =. |
|00000490| 20 20 20 31 2e 33 33 20 | 20 0d 20 20 20 20 20 31 | 1.33 | . 1|
|000004a0| 2e 36 36 20 20 0d 20 20 | 20 20 20 31 2e 35 38 20 |.66 . | 1.58 |
|000004b0| 20 0d 20 20 20 20 30 2e | 39 33 33 20 20 0d 3e 20 | . 0.|933 .> |
|000004c0| 42 20 3d 20 5b 42 31 2c | 42 32 5d 0d 20 42 20 3d |B = [B1,|B2]. B =|
|000004d0| 0d 20 20 20 20 30 2e 35 | 39 35 20 20 20 20 20 20 |. 0.5|95 |
|000004e0| 20 31 2e 33 33 20 20 0d | 20 20 20 20 30 2e 38 34 | 1.33 .| 0.84|
|000004f0| 36 20 20 20 20 20 20 20 | 31 2e 36 36 20 20 0d 20 |6 |1.66 . |
|00000500| 20 20 20 30 2e 37 39 31 | 20 20 20 20 20 20 20 31 | 0.791| 1|
|00000510| 2e 35 38 20 20 0d 20 20 | 20 20 30 2e 33 32 39 20 |.58 . | 0.329 |
|00000520| 20 20 20 20 20 30 2e 39 | 33 33 20 20 0d 3e 20 46 | 0.9|33 .> F|
|00000530| 20 3d 20 66 61 63 74 6f | 72 28 41 29 0d 20 20 20 | = facto|r(A). |
|00000540| 6c 75 20 20 20 20 20 20 | 20 20 20 20 20 70 76 74 |lu | pvt|
|00000550| 20 20 20 20 20 20 20 20 | 20 20 72 63 6f 6e 64 20 | | rcond |
|00000560| 20 20 20 20 20 20 20 0d | 3e 20 62 61 63 6b 73 75 | .|> backsu|
|00000570| 62 28 46 2c 42 29 0d 20 | 20 20 20 30 2e 38 31 32 |b(F,B). | 0.812|
|00000580| 20 20 20 20 20 20 30 2e | 36 39 37 20 20 0d 20 20 | 0.|697 . |
|00000590| 20 20 30 2e 35 34 33 20 | 20 20 20 20 20 30 2e 31 | 0.543 | 0.1|
|000005a0| 33 37 20 20 0d 20 20 20 | 20 30 2e 32 35 34 20 20 |37 . | 0.254 |
|000005b0| 20 20 20 20 30 2e 38 31 | 35 20 20 0d 20 20 20 30 | 0.81|5 . 0|
|000005c0| 2e 30 38 32 35 20 20 20 | 20 20 20 30 2e 39 37 34 |.0825 | 0.974|
|000005d0| 20 20 0d 3e 20 2f 2f 20 | 54 68 69 73 20 69 73 20 | .> // |This is |
|000005e0| 5b 58 31 2c 58 32 5d 20 | 2d 20 73 6f 20 69 74 20 |[X1,X2] |- so it |
|000005f0| 77 6f 72 6b 73 21 0d 5c | 65 6e 64 7b 76 65 72 62 |works!.\|end{verb|
|00000600| 61 74 69 6d 7d 0d 0d 53 | 65 65 20 61 6c 73 6f 3a |atim}..S|ee also:|
|00000610| 20 50 61 67 65 7e 5c 70 | 61 67 65 72 65 66 7b 66 | Page~\p|ageref{f|
|00000620| 6e 3a 66 61 63 74 6f 72 | 7d 20 5c 76 65 72 62 2b |n:factor|} \verb+|
|00000630| 66 61 63 74 6f 72 28 29 | 2b 2c 0d 50 61 67 65 7e |factor()|+,.Page~|
|00000640| 5c 70 61 67 65 72 65 66 | 7b 66 6e 3a 69 6e 76 7d |\pageref|{fn:inv}|
|00000650| 20 5c 76 65 72 62 2b 69 | 6e 76 28 29 2b 2c 0d 50 | \verb+i|nv()+,.P|
|00000660| 61 67 65 7e 5c 70 61 67 | 65 72 65 66 7b 66 6e 3a |age~\pag|eref{fn:|
|00000670| 73 6f 6c 76 65 7d 20 5c | 76 65 72 62 2b 73 6f 6c |solve} \|verb+sol|
|00000680| 76 65 28 29 2b 2e 0d 0d | 5c 6e 65 77 70 61 67 65 |ve()+...|\newpage|
|00000690| 0d 0d 0d 0d 0d 0d | |...... | |
+--------+-------------------------+-------------------------+--------+--------+