4.1 Basis for R6 Skal bestemme en basis for R6 indeholdende pr\303\246cis tre af de givne vektorer. Derudover skal jeg selv tilf\303\270je de manglende vektorer (der er n\303\270dt til at v\303\246re 6 for at de kan spanne hele R6). Definerer mine vektorer inden i en matrix som v\303\246rende s\303\270jlerne i denne og ser hvordan den ser ud som v\303\246rende reduceret trappematrix: restart: with(LinearAlgebra): A[1]:=< <3|0|-2|3>,<2|1|-2|0>,<0|0|-2|3>,<0|0|2|-3>,<1|1|0|-3>,<-1|1|0|-3> >;

PiUjQTFHLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRik2JVEiP0YpLyUnaXRhbGljR1EldHJ1ZUYpLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKQ==

ReducedRowEchelonForm(A[1]);

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiP0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

S\303\246tter sammen med en identitetsmatrice og reducerer denne s\303\245 jeg kan se p\303\245 ledende 1-taller: A[2]:=<A[1]|IdentityMatrix(6)>;

PiUjQTJHLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRik2JVEiP0YpLyUnaXRhbGljR1EldHJ1ZUYpLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKQ==

ReducedRowEchelonForm(A[2]);

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiP0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

Jeg skal alts\303\245 bruge s\303\270jlerne svarende til s\303\270jle 1, 2, 3, 5, 6 og 7 ovenfor: Column(A[2],1),Column(A[2],2),Column(A[2],3),Column(A[2],5),Column(A[2],6),Column(A[2],7);

NigtSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGKDYlUSI/RigvJSdpdGFsaWNHUSV0cnVlRigvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoRiNGI0YjRiNGIw==

Jeg s\303\246tter disse sammen i en matrix: A[3]:=SubMatrix(A[2],[1..6],[1,2,3,5,6,7]);

PiUjQTNHLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRik2JVEiP0YpLyUnaXRhbGljR1EldHJ1ZUYpLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKQ==

Jeg skal nu huske at den sidste af de fire vektorer er givet ved: X:=< <3>,<0>,<3>,<-3>,<-3>,<-3> >;

PiUiWEctSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGKTYlUSI/RikvJSdpdGFsaWNHUSV0cnVlRikvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yp

Og jeg kan nu finde dennes koordinater i min base A3 ved at l\303\270se ligningssystemet som f\303\270lger, hvor jeg s\303\245 finder den sidste s\303\270jle til at v\303\246re koordinaterne, udskrevet med Column(): A[4]:=<A[3]|X>;

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

ReducedRowEchelonForm(A[4]); Column(%,7);

LUkobWFjdGlvbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUklbXJvd0dGJDYnLUknbXRhYmxlR0YkNjotSSRtdHJHRiQ2LC1JJG10ZEdGJDYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGQy8lK2dyb3VwYWxpZ25HRkMvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGSi1GODYoLUY7NiRRIjBGJ0Y+RkFGREZGRkhGS0ZNRk1GTUZNRk1GQUZERkYtRjU2LEZNRjdGTUZNRk1GTS1GODYoLUYvNigtSSNtb0dGJDYtUSomdW1pbnVzMDtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Zobi8lKXN0cmV0Y2h5R0Zobi8lKnN5bW1ldHJpY0dGaG4vJShsYXJnZW9wR0Zobi8lLm1vdmFibGVsaW1pdHNHRmhuLyUnYWNjZW50R0Zobi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmdvLUY7NiRRIjNGJ0Y+LyUlc2l6ZUdRIzEyRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRmhuRj5GQUZERkZGSEZLRkFGREZGLUY1NixGTUZNRjdGTUZNRk0tRjg2KC1GLzYoRlgtSSZtZnJhY0dGJDYoRmpvLUY7NiRRIjJGJ0Y+LyUubGluZXRoaWNrbmVzc0dGSi8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZlcS8lKWJldmVsbGVkR0ZobkZdcEZgcEZjcEY+RkFGREZGRkhGS0ZBRkRGRi1GNTYsRk1GTUZNRjdGTUZNRk1GQUZERkYtRjU2LEZNRk1GTUZNRjdGTUZNRkFGREZGLUY1NixGTUZNRk1GTUZNRjdGTUZBRkRGRi8lJmFsaWduR1ElYXhpc0YnL0ZCUSliYXNlbGluZUYnL0ZFRmVxL0ZHUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdRJXRydWVGJy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl1zLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmhzLyUmZnJhbWVHRmhzLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGaG4vJS1lcXVhbGNvbHVtbnNHRmhuLyUtZGlzcGxheXN0eWxlR0Zobi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zlc0ZdcEZgcEZjcEY+Rj4vSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZbdS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE2Njc1OTUyNEYn

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

Hvilket er det samme som at sige: A[3]^(-1).X;

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

4.2 R\303\246kkerum, s\303\270jlerum og nulrum Skal bestemme r\303\246kkerum, s\303\270jlerum og nulrum for en given matrix: restart: with(LinearAlgebra): A:=< <1|2|1|3|4>,<0|1|2|1|0>,<2|3|-1|4|6>,<0|0|1|1|2> >;

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKjtFIVw7

GaussianElimination(A);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKj94U2wi

ReducedRowEchelonForm(A);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKks2W2wi

R\303\246kkerum findes: RowSpace(A);

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

S\303\270jlerum findes: ColumnSpace(A);

NyUtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIionNDNcOy1GJDYjL0YuIipPIjNcOy1GJDYjL0YuIip3IjNcOw==

Til sidst nulrummet: NullSpace(A);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYpLUkobWFjdGlvbkdGJDYlLUYjNigtRiw2Jy1JJ210YWJsZUdGJDY5LUkkbXRyR0YkNiYtSSRtdGRHRiQ2KC1GLDYoLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlgtSSNtbkdGJDYkUSI0RidGRC8lJXNpemVHUSMxMkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZJRkQvJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRmNvLyUrZ3JvdXBhbGlnbkdGY28vJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGam9GYW9GZG9GZm8tRjk2Ji1GPDYoLUZmbjYkUSIxRidGREZhb0Zkb0Zmb0Zob0ZbcEZhb0Zkb0Zmby1GOTYmLUY8NigtRiw2KEZARmFwRmluRlxvRl9vRkRGYW9GZG9GZm9GaG9GW3BGYW9GZG9GZm9GXXAtRjk2Ji1GPDYoLUZmbjYkUSIwRidGREZhb0Zkb0Zmb0Zob0ZbcEZhb0Zkb0Zmby8lJmFsaWduR1ElYXhpc0YnL0Zib1EpYmFzZWxpbmVGJy9GZW9RJnJpZ2h0RicvRmdvUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdRJXRydWVGJy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl9yLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmpyLyUmZnJhbWVHRmpyLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGSS8lLWVxdWFsY29sdW1uc0dGSS8lLWRpc3BsYXlzdHlsZUdGSS8lJXNpZGVHRmdxLyUwbWlubGFiZWxzcGFjaW5nR0ZnckZpbkZcb0Zfb0ZERkQvSSttc2VtYW50aWNzR0YkUSpDb2xWZWN0b3JGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZcdC8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE2NDM1MjY2NEYnLUZBNi1RIixGJ0ZERkcvRktGXHJGTEZORlBGUkZUL0ZXUSYwLjBlbUYnL0ZaUSwwLjMzMzMzMzNlbUYnLUYvNiUtRiM2KC1GLDYnLUY2NjktRjk2Ji1GPDYoLUYsNihGQC1GZm42JFEjMTBGJ0ZERmluRlxvRl9vRkRGYW9GZG9GZm9GaG9GW3BGYW9GZG9GZm8tRjk2Ji1GPDYoRmVuRmFvRmRvRmZvRmhvRltwRmFvRmRvRmZvLUY5NiYtRjw2KC1GLDYoRkAtRmZuNiRRIjJGJ0ZERmluRlxvRl9vRkRGYW9GZG9GZm9GaG9GW3BGYW9GZG9GZm9GanBGXXBGYXFGZHFGZnFGaHFGanFGXXJGYHJGYnJGZXJGaHJGW3NGXXNGX3NGYnNGZHNGZnNGaHNGanNGaW5GXG9GX29GREZERlx0Rl90RmJ0Rlx0RmV0L0ZpdFEqMTY0MzgzNTE2RidGaW5GXG9GX29GREZEL0ZgdFEifGZyRicvRmN0USJ8aHJGJw==

Vil se om de er det samme som dem jeg har fundet i h\303\245nden: H:=<<1|2|1>,<0|1|2>,<2|3|-1>,<0|0|1>>;

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKl9cV3gi

M:=<<1|0|0>,<0|1|0>,<0|0|1>,<2|-1|-1>>;

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKk8vK20i

ReducedRowEchelonForm(H);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKms0LGwi

ReducedRowEchelonForm(H); JSFH TTdSMApJNlJUQUJMRV9TQVZFLzE2NDkwMjYxNlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzUiJSImIiIiIiIhIiIjRihGKUYnIiIkRihGJ0YpISIiRidGKkYnIiIlRidGLEYoIiInRilGJg==TTdSMApJNlJUQUJMRV9TQVZFLzE2NTQwNzcyMFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzUiJSImIiIiIiIhRihGKCIiI0YnRihGKEYnRikhIiJGKCIiJEYnRipGKCIiJUYoISIjRihGJg==TTdSMApJNlJUQUJMRV9TQVZFLzE2NTQ4MTEzMlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzUiJSImIiIiIiIhRihGKEYoRidGKEYoRihGKEYnRigiIiUhIiJGJ0YoIiM1ISIlIiIjRihGJg==TTdSMApJNlJUQUJMRV9TQVZFLzE2NDkwODA5NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIiIiIUYoIiIjRiY=TTdSMApJNlJUQUJMRV9TQVZFLzE2NDkwODEzNlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiISIiIkYnISIiRiY=TTdSMApJNlJUQUJMRV9TQVZFLzE2NDkwODE3NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSIiIUYnIiIiISIiRiY=TTdSMApJNlJUQUJMRV9TQVZFLzE3NzQ0NDk1MlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJSIkIiIiIiIhIiIjRihGKUYnIiIkRihGJ0YpISIiRidGJg==TTdSMApJNlJUQUJMRV9TQVZFLzE2NjAwMDQzNlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJSIkIiIiIiIhRigiIiNGKEYnRighIiJGKEYoRidGKkYmTTdSMApJNlJUQUJMRV9TQVZFLzE2NTAxMDk2NFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJSIkIiIiIiIhRihGKEYoRidGKEYoRihGKEYnRihGJg==