2016年6月17日金曜日

数学 - 線型代数 - ベクトル空間 - 基底と次元(座標、3次元(2))

• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

$\begin{array}{l}a=\left({a}_{1},{a}_{2},{a}_{3}\right)\\ b=\left({b}_{1},{b}_{2},{b}_{3}\right)\\ c=\left({c}_{1},{c}_{2},{c}_{3}\right)\\ 0a+1b+1c=\left(1,0,0\right)\\ 1a+0b+1c=\left(0,1,0\right)\\ 1a+1b+0c=\left(0,0,1\right)\\ \left({b}_{1}+{c}_{1},{b}_{2}+{c}_{2},{b}_{3}+{c}_{3}\right)=\left(1,0,0\right)\\ \left({a}_{1}+{c}_{1},{a}_{2}+{c}_{2},{a}_{3}+{c}_{3}\right)=\left(0,1,0\right)\\ \left({a}_{1}+{b}_{1},{a}_{2}+{b}_{2},{a}_{3}+{b}_{3}\right)=\left(0,0,1\right)\\ {b}_{1}=-{a}_{1}\\ {b}_{2}=-{a}_{2}\\ {c}_{1}=-{a}_{1}\\ {c}_{3}=-{a}_{3}\\ {c}_{2}=-{b}_{2}={a}_{2}\\ {b}_{3}=-{c}_{3}={a}_{3}\\ -{a}_{1}-{a}_{1}=1\\ {a}_{1}=-\frac{1}{2}\\ {a}_{2}+{a}_{2}=1\\ {a}_{2}=\frac{1}{2}\\ {a}_{3}+{a}_{3}=1\\ {a}_{3}=\frac{1}{2}\\ a=\left(-\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\\ b=\left(\frac{1}{2},-\frac{1}{2},\frac{1}{2}\right)\\ c=\left(\frac{1}{2},\frac{1}{2},-\frac{1}{2}\right)\end{array}$