Quod Erat Demonstrandum

2017/04/22

逆矩陣

Filed under: mathematics,NSS,University Mathematics — johnmayhk @ 11:10 下午
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$AB=BA=I$

2017/04/21

三垂線定理

Filed under: mathematics,NSS,Pure Mathematics,University Mathematics — johnmayhk @ 12:56 下午
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（一）前言

2017/04/17

人類總是

Filed under: mathematics — johnmayhk @ 6:12 下午

#無聊慎入

Solve $\frac{1}{2}(x-1)=3$.

$\frac{1}{2}x=3+1$ (more…)

2017/04/16

行列式特性

Filed under: NSS,Pure Mathematics — johnmayhk @ 5:05 下午
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Factorize $\left|\begin{array}{rcl}a &b &c\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$.

$\left|\begin{array}{rcl}a+b+c &a+b+c &a+b+c\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$

$=(a+b+c)\left|\begin{array}{rcl}1 &1 &1\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$

$\left|\begin{array}{rcl}a &b-a &c-a\\b+c &a-b &a-c \\a^2 &b^2-a^2 &c^2-a^2\\\end{array}\right|$

2017/04/05

答問

Filed under: Junior Form Mathematics — johnmayhk @ 11:11 下午
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$\displaystyle \frac{a}{(b-c)^2}+\frac{b}{(c-a)^2}+\frac{c}{(a-b)^2}=0$

$\displaystyle \frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}$