From d75c78b1d6905c68adcf5b65e7d8bac3038b2a84 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Wed, 7 Jul 2021 23:13:52 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E7=BA=BF=E6=80=A7=E6=96=B9?= =?UTF-8?q?=E7=A8=8B=E7=BB=84?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- linear-algebra/exercise/3-vector/vector.pdf | Bin 68481 -> 68563 bytes linear-algebra/exercise/3-vector/vector.tex | 2 + linear-algebra/knowledge/2-matrix/matrix.pdf | Bin 120267 -> 119954 bytes linear-algebra/knowledge/2-matrix/matrix.tex | 5 +- linear-algebra/knowledge/3-vector/vector.pdf | Bin 75056 -> 75074 bytes linear-algebra/knowledge/3-vector/vector.tex | 2 +- .../linear-equations-system.pdf | Bin 68980 -> 112078 bytes .../linear-equations-system.tex | 249 +++++++++++++++++- 8 files changed, 251 insertions(+), 7 deletions(-) diff --git a/linear-algebra/exercise/3-vector/vector.pdf b/linear-algebra/exercise/3-vector/vector.pdf index 9fd310d92c8324b494675829859eb1738c14370f..81fe7f017ad11eaa5dc83d411c7d131f73473ec4 100644 GIT binary patch delta 18465 zcmY(pV{j(S^934P8{66#Pi)(^Z97k#jcwbuZEuo|ZQHu<{n!0)e^oP8T{ZJzrf24K zpVJeV2C4VC}QHcdydL zZ&3EmTnnXEgAB|Xxk&l@M_$@j{7(3a2Q=~x2r4Q>&DB-%V^&FW00HxsZ_qJAqigxT zmh1+HBXjp}7B6pJw?EGxXB}_Xb+w>nCQJwNP38ofo*>#AJh7< z={{+>c+wCc#lu-7J~BAZ(|r3~94!EOH%A_MJwOV%yW|=1N?(xh5_|}Aoul5#&Zu;r zFWrrX%==%eQQJmKsMnYs)&`cmS-;B$i@pAO-Yv$uyQj&_E!Br$=LhV3EByuAC6Y)C z8hRDVWkwc8P$PS@$^llD(GWD+geeX&qaAyHU6uw=4(~$~BqrMVkb4PR-{3&>0Dtij zE|KMLtELYX45BJ(D4Gh-A7dLC#EByK@8$yHmSD6fxhp1}Kp|;m8fc6mG%!n~lHNXp z0vC_Gg7TaE=k@or$lfBu?bP`a%IJIe%>JEsQb2mkALH`5 z8{#yu9z|9cqO=!Zw*9|`AnPK>G=n0m4M8~zg%+2vTF0b)0jILRU29I<3ubfkZzNUl zbofQ?ODhcNIyMSSu%^3u#zG3D+-zmo6J4<2bKN=J!OAKmcD^L`rE#Bypdi?a8*Vh0 z9f0nQ-{%lI+jRP;PE4X_{>~YGzY@|ZF%OtWAs}ETbl;9L%}sD8W@wBUp`#hknP&@) z8KS9$TnMT4(TbWcb}p+1+iz=DOj`}p`KOGSC|W1h;zp}x9)2upg(jJNhv5tNtK)ET zIek3F9t9)?$uD6W2iiq7WC1Wd`NniB=xQuF!{nH7l%uk1IZC@>=jTryH#Ke@h6waF z)4j2%;Z1m??<6Q^mE$u#dexx=6JsSS(Dez+sad5laXKB8KGBkR>lKQ;TDH?uGN@y2 z6J!vME04BimQ6mG-)8Ko|lYWQRhUN2I`;gaZBG@8|*!O&;?o3Ih@rS-A zfIgfI6{|@EoA!@Y5A9JO0TDcX*90c0$Lf{p=_=FWG(&f()_998i#=u}Np0%)80H&< z`;nO`p}LYMOHX|NX^0xaCL>B#STjKlYv}>-^QF9FC7~*LA+Ru0j$Y z2OmG$SOs8yuwcvZEBy**>xtrM2*nWgNbMc$?zY~O5M|f0tT~s~wM`28r7)-c19QoCGtH9TZeiW5P5J5A4R!6N2Dmxz^b z8Z>Udw)F&6Cq$o!792A>b_B@o4X7E&CAO-2#-}_0ZG(FpyHZ@oc_7l_>AusG z=kcm3G;rTKI^7y2mh=;j=l}vOj3V^0>;!fWgd;!x^E&hQyTuM&_B+MsRozx9)%S`U z{g7+Boay62U=bgS7VIRulx|=~HtY6nqitI(E#OAlU61qTrY1&fuWIjYo{i8|j$8XE zR}o!y4op#nu?W?bQ^4}EV`Xu^XS+!N*@s6R;83XBCjDFSZ;R_gf0(pwG4!u78w9I= z(i|t%gKLjX2m-ac;m|Ib!;G8Hhm$Q;PrOM9Cb(&!|7-3P_3GjH4IR2YZlvVSt{#X9gDF)mw@?f%)!p? 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$k\alpha=[ka_1,ka_2,\cdots,ka_3]$。 \subsection{概念} -极大线性无关组\textcolor{violet}{\textbf{定义:}}在向量组$\alpha_1,\alpha_2,\cdots,\alpha_n$中,若存在部分$a_i,a_j,\cdots,a_k$满足:\ding{172}$a_i,a_j,\cdots,a_k$线性无关。\ding{173}向量组中任一向量$a_s$($i=1,2,\cdots,n$)均可由$a_i,a_j,\cdots,a_k$线性表出。则称向量组$a_i,a_j,\cdots,a_k$为原向量组的极大线性无关组。 +极大线性无关组\textcolor{violet}{\textbf{定义:}}在向量组$\alpha_1,\alpha_2,\cdots,\alpha_n$中,若存在部分$a_i,a_j,\cdots,a_k$满足:\ding{172}$a_i,a_j,\cdots,a_k$线性无关;\ding{173}向量组中任一向量$a_s$($i=1,2,\cdots,n$)均可由$a_i,a_j,\cdots,a_k$线性表出,则称向量组$a_i,a_j,\cdots,a_k$为原向量组的极大线性无关组。 不包含无用约束方程的最简方程组的系数矩阵就是极大线性无关组。 diff --git a/linear-algebra/knowledge/4-linear-equations-system/linear-equations-system.pdf b/linear-algebra/knowledge/4-linear-equations-system/linear-equations-system.pdf index c65ef8b3fbccb7a6ab8167621789cde026293433..c5854a48f00ff312bc9d1315ae832653560eec32 100644 GIT binary patch delta 108001 zcmZ^~V{l+Wzx6vwCf3AGCQc@{ZQHhO?ul*NwylY6+fF8Sa_2nveXGu?bMJ?}t83Tl 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