三階行列式的展開
Author: 藍邦偉  老師

三階行列式的展開(Sarus降階法)拉動s重新整理

s = 0.5 (slider from 0 to 1, step 0.1)
a_2: Random[-5, 5] + s * 0
a_3: Random[-5, 5] + s * 0
b_1: Random[-5, 5] + s * 0
b_2: Random[-5, 5] + s * 0
b_3: Random[-5, 5] + s * 0
c_1: Random[-5, 5] + s * 0
a_1: Random[-5, 5] + s * 0
c_2: Random[-5, 5] + s * 0
c_3: Random[-5, 5] + s * 0
text1: "\left|\begin{array}{rr}" + a_1 + " &" + a_2 + "  &" + a_3 + "  \\ " + b_1 + "  &" + b_2 + "  &" + b_3 + "  \\ " + c_1 + "&" + c_2 + "  & " + c_3 + " \\ \end{array}\right|"
文字1: "= (" + (LaTeX[a_1]) + ")(" + (LaTeX[b_2]) + ")(" + (LaTeX[c_3]) + ")+(" + (LaTeX[a_2]) + ")(" + (LaTeX[b_3]) + ")(" + (LaTeX[c_1]) + ")+(" + (LaTeX[a_3]) + ")(" + (LaTeX[b_1]) + ")(" + (LaTeX[c_2]) + ")-(" + (LaTeX[a_3]) + ")(" + (LaTeX[b_2]) + ")(" + (LaTeX[c_1]) + ")-(" + (LaTeX[a_2]) + ")(" + (LaTeX[b_1]) + ")(" + (LaTeX[c_3]) + ")-(" + (LaTeX[a_1]) + ")(" + (LaTeX[b_3]) + ")(" + (LaTeX[c_2]) + ")"
文字3: "= " + (LaTeX[a_1 * b_2 * c_3]) + "" + (LaTeX[If[a_2 * b_3 * c_1 < 0, "-", "+"]]) + "" + (LaTeX[abs(a_2 * b_3 * c_1)]) + "" + (LaTeX[If[a_3 * b_1 * c_2 < 0, "-", "+"]]) + "" + (LaTeX[abs(a_3 * b_1 * c_2)]) + "" + (LaTeX[If[a_3 * b_2 * c_1 < 0, "+", "-"]]) + "" + (LaTeX[abs(a_3 * b_2 * c_1)]) + "" + (LaTeX[If[a_2 * b_1 * c_3 < 0, "+", "-"]]) + "" + (LaTeX[abs(a_2 * b_1 * c_3)]) + "" + (LaTeX[If[a_1 * b_3 * c_2 < 0, "+", "-"]]) + "" + (LaTeX[abs(a_1 * b_3 * c_2)]) + ""
文字4: "= " + (LaTeX[a_1 * b_2 * c_3 + a_2 * b_3 * c_1 + a_3 * b_1 * c_2 - a_3 * b_2 * c_1 - a_2 * b_1 * c_3 - a_1 * b_3 * c_2]) + ""