三階行列式的降階(2)
Author: 藍邦偉  老師

三階行列式的展開(La'Place降階法):拉動s改變亂數

對第一列展開

對第一行展開

對第二列展開

對第二行展開

對第三列展開

對第三行展開

s = 0.9 (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
a_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
c_2: Random[-5, 5] + s * 0
c_3: Random[-5, 5] + s * 0
n = 0 (slider from 0 to 6, step 1)
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A = (-7569670.119876427, -3779094.1127364496)
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文字6: "=" + (LaTeX[a_1]) + "\left|\begin{array}{cc}" + (LaTeX[b_2]) + " &" + (LaTeX[b_3]) + " \\" + (LaTeX[c_2]) + " &" + (LaTeX[c_3]) + " \\ \end{array}\right|-(" + (LaTeX[b_1]) + ")\left|\begin{array}{cc} " + (LaTeX[a_2]) + " &" + (LaTeX[a_3]) + " \\" + (LaTeX[c_2]) + " &" + (LaTeX[c_3]) + " \\ \end{array}\right|+(" + (LaTeX[c_1]) + ")\left|\begin{array}{cc}" + (LaTeX[a_2]) + " &" + (LaTeX[a_3]) + " \\" + (LaTeX[b_2]) + " &" + (LaTeX[b_3]) + " \\ \end{array}\right|=" + (LaTeX[a_1]) + "(" + (LaTeX[If[b_2 * c_3 - c_2 * b_3 < 0, "-", "+"]]) + "" + (LaTeX[abs(b_2 * c_3 - b_3 * c_2)]) + ")" + (LaTeX[If[b_1 < 0, "+", "-"]]) + "" + (LaTeX[abs(b_1)]) + "(" + (LaTeX[If[a_2 * c_3 - c_2 * a_3 < 0, "-", "+"]]) + "" + (LaTeX[abs(a_2 * c_3 - a_3 * c_2)]) + ")" + (LaTeX[If[c_1 < 0, "-", "+"]]) + "" + (LaTeX[abs(c_1)]) + "(" + (LaTeX[If[a_2 * b_3 - a_3 * b_2 > 0, "+", "-"]]) + "" + (LaTeX[abs(a_2 * b_3 - a_3 * b_2)]) + ")=" + (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]) + ""
文字15: "=-(" + (LaTeX[a_2]) + ")\left|\begin{array}{cc}" + (LaTeX[b_1]) + " &" + (LaTeX[b_3]) + " \\" + (LaTeX[c_1]) + " &" + (LaTeX[c_3]) + " \\ \end{array}\right|+(" + (LaTeX[b_2]) + ")\left|\begin{array}{cc} " + (LaTeX[a_1]) + " &" + (LaTeX[a_3]) + " \\" + (LaTeX[c_1]) + " &" + (LaTeX[c_3]) + " \\ \end{array}\right|-(" + (LaTeX[c_2]) + ")\left|\begin{array}{cc}" + (LaTeX[a_1]) + " &" + (LaTeX[a_3]) + " \\" + (LaTeX[b_1]) + " &" + (LaTeX[b_3]) + " \\ \end{array}\right|=" + (LaTeX[If[a_2 > 0, "-", "+"]]) + "" + (LaTeX[abs(a_2)]) + "(" + (LaTeX[If[b_1 * c_3 - c_1 * b_3 < 0, "-", "+"]]) + "" + (LaTeX[abs(b_1 * c_3 - b_3 * c_1)]) + ")" + (LaTeX[If[b_2 < 0, "-", "+"]]) + "" + (LaTeX[abs(b_2)]) + "(" + (LaTeX[If[a_1 * c_3 - c_1 * a_3 < 0, "-", "+"]]) + "" + (LaTeX[abs(a_1 * c_3 - a_3 * c_1)]) + ")" + (LaTeX[If[c_2 > 0, "-", "+"]]) + "" + (LaTeX[abs(c_2)]) + "(" + (LaTeX[If[a_1 * b_3 - a_3 * b_1 > 0, "+", "-"]]) + "" + (LaTeX[abs(a_1 * b_3 - a_3 * b_1)]) + ")=" + (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]) + ""
文字23: "=" + (LaTeX[a_3]) + "\left|\begin{array}{cc}" + (LaTeX[b_1]) + " &" + (LaTeX[b_2]) + " \\" + (LaTeX[c_1]) + " &" + (LaTeX[c_2]) + " \\ \end{array}\right|-(" + (LaTeX[b_3]) + ")\left|\begin{array}{cc} " + (LaTeX[a_1]) + " &" + (LaTeX[a_2]) + " \\" + (LaTeX[c_1]) + " &" + (LaTeX[c_2]) + " \\ \end{array}\right|+(" + (LaTeX[c_3]) + ")\left|\begin{array}{cc}" + (LaTeX[a_1]) + " &" + (LaTeX[a_2]) + " \\" + (LaTeX[b_1]) + " &" + (LaTeX[b_2]) + " \\ \end{array}\right|=" + (LaTeX[a_3]) + "(" + (LaTeX[If[b_1 * c_2 - c_1 * b_2 < 0, "-", "+"]]) + "" + (LaTeX[abs(b_1 * c_2 - b_2 * c_1)]) + ")" + (LaTeX[If[b_3 < 0, "+", "-"]]) + "" + (LaTeX[abs(b_3)]) + "(" + (LaTeX[If[a_1 * c_2 - c_1 * a_2 < 0, "-", "+"]]) + "" + (LaTeX[abs(a_1 * c_2 - a_2 * c_1)]) + ")" + (LaTeX[If[c_3 < 0, "-", "+"]]) + "" + (LaTeX[abs(c_3)]) + "(" + (LaTeX[If[a_1 * b_2 - a_2 * b_1 > 0, "+", "-"]]) + "" + (LaTeX[abs(a_1 * b_2 - a_2 * b_1)]) + ")=" + (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]) + ""
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