From b2887d47b9f5def9787edbc921ace39ba44e79b0 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Fri, 14 Oct 2022 23:30:34 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- linear-algebra/exercise/3-vector/vector.pdf | Bin 86668 -> 87379 bytes linear-algebra/exercise/3-vector/vector.tex | 10 ++++++---- linear-algebra/exercise/5-similar/similar.pdf | Bin 97138 -> 97864 bytes linear-algebra/exercise/5-similar/similar.tex | 8 ++++++++ .../6-quadratic-form/quadratic-form.pdf | Bin 86471 -> 86944 bytes .../6-quadratic-form/quadratic-form.tex | 6 ++++-- .../knowledge/5-similar/similar.pdf | Bin 101431 -> 101477 bytes .../knowledge/5-similar/similar.tex | 1 + .../6-quadratic-form/quadratic-form.pdf | Bin 92968 -> 92977 bytes 9 files changed, 19 insertions(+), 6 deletions(-) diff --git a/linear-algebra/exercise/3-vector/vector.pdf b/linear-algebra/exercise/3-vector/vector.pdf 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+基本是证明题,若证明$\alpha$、$\beta$线性无关,则令$k_1\alpha+k_2\beta=0$,判断$k_i$的值,如果只有零解则代表$k$矩阵为满秩,从而线性无关。 + +\subsubsection{代入重组} 若要求线性相关的式子由其他向量构成,则将式子代入表示目标式子。 @@ -70,7 +72,7 @@ $\therefore k_1+k_2+3k_3=0$,且$k_1-2k_2+2k_3=0$即可。 而未知数的个数大于方程个数,所以有无穷多解,从而必然有非零解,从而$\beta_1$,$\beta_2$,$\beta_3$线性相关。 -\subsection{同乘} +\subsubsection{同乘} 若要求线性相关的式子存在一定的乘积关系,则可以用同乘一步步消去系数。 diff --git a/linear-algebra/exercise/5-similar/similar.pdf b/linear-algebra/exercise/5-similar/similar.pdf index 45616b2d8fd97a337e814738782aa0cfddf51f19..a811c77f4d30727722f0ba96716286bbafdbac62 100644 GIT binary patch delta 67712 zcmZU(V~lQF8!Woowr$(CZQHi_wyo8+ZLG#>+qP}nxO?w&b927jWXz;8GyV*uo~ozD z{WI9;Cm0f$qNq3>6FnO=+2QTgD>MuHZzNIx6C)E7KR>jKtFxJr9kl2Am9|{`A|q_q z1I;@G`)XVc0@M`{R6-lk6`Yf0nTkB_>kr1})|vIZtwmxZ2(Va@5{sI$&!_&CM%mU3 zJkKnGdoK4)Ayfm;=PXLz=^<5 zn}LBOjQIkNkbVVy&;e0zHwJNI%}v8(M%sx)fju5k6fyjqe!~PeHlam<22L{9caX%% zC-TajTT|jkl=0m@FF4SLhnw84cZL;!91GWgA%|^U+WJGuGS+Q14IO3nYo~J0-lPw& zfylPwBgKu-?EdV`1Bvl3R31H!DjQkIuU 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-解:从四个选项,由于是常量矩阵,所以由对角线元素的正负号可以得出这四个的惯性系数分别为$(3,0)$、$(2,1)$、$(1,2)$、$0,3$(前面为正惯性系数,后面为负惯性系数)。 +解:从四个选项,由于是常量矩阵,所以由对角线元素的正负号可以得出这四个的惯性系数分别为$(3,0)$、$(2,1)$、$(1,2)$、$(0,3)$(前面为正惯性系数,后面为负惯性系数)。 且每个选项的秩都是3。 diff --git a/linear-algebra/knowledge/5-similar/similar.pdf b/linear-algebra/knowledge/5-similar/similar.pdf index 997213018f057caa11366d96e053856af7404288..373f77dfa206e035922fa009cb901cb35ce8a107 100644 GIT binary patch delta 23213 zcmY(q1Cu6P6D&Aw+qP}nwr$&drfu7{ZQHhO8`Hh-ez6;I?@u@xm06XQr`poNPtw8T z*@4-)8aOY20ZcWLz}30pkFt+()i5P9bWpsh;l%A#@rrkXGwAW<6)+fm-nifBl9D+1 zzR9m`5Cm?G7(zN^K9BfGZc?w2evZ#ejE*wol(zO6`wf!Gfzm!a`TntrrIOEVzYUz( zje^gl_p`Z#A1jiXpN(dJGqzD0iuph+pMRKUHv2x|Y!v7IAhlD0B(t}{-fNOd3#}0n z?HWMS5h^XgT*HGLDk&g{N$_IdflCv#ZUyKBra9LjZFl>T>LPdlhJOVto~DA}M~PBV z)(H}CUBor5MU;Dn_ZBkH%GwL^qK6C5is6qQ-3feyI54EbH^G65;{rICIQjXZU0j{b zjO?I2H+Qs@9FEvw{rBqbO?U`1C6x+;U!Zlvwt##(;kxT}|2{UYa@+K&$6BaiXq?XnyqBu!?J0=jgt?@>Q^m;+-Oz`AX%)>xI!&5r#&}ZG 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