三階克拉瑪公式
Author: 藍邦偉  老師

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克拉瑪公式

\left\lbrace  \begin{array}{r} a_1x+b_1y+c_1z=d_1 \ a_2x+b_2y+c_2z=d_2 \ a_3x+b_3y+c_3z=d_3 \ \end{array}\right.

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無解：\left\lbrace \begin{array}{ll} 三平面兩兩相交，交線不共點  \  兩平面平行，另一平面與其交與兩平行線 \ \end{array}  \right.\ 

可能無解也可能無限多解

a1 = 0 (slider from -5 to 5, step 1)
b1 = 0 (slider from -5 to 5, step 1)
c1 = 0 (slider from -5 to 5, step 1)
d1 = 0 (slider from -5 to 5, step 1)
a2 = 0 (slider from -5 to 5, step 1)
b2 = 0 (slider from -5 to 5, step 1)
c2 = 0 (slider from -5 to 5, step 1)
d2 = 0 (slider from -5 to 5, step 1)
a3 = 0 (slider from -5 to 5, step 0.1)
b3 = 0 (slider from -5 to 5, step 1)
c3 = 0 (slider from -5 to 5, step 1)
d3 = 0 (slider from -5 to 5, step 1)
A1 = Textfield(a1)
B1 = Textfield(b1)
C1 = Textfield(c1)
D1 = Textfield(d1)
A2 = Textfield(a2)
B2 = Textfield(b2)
C2 = Textfield(c2)
D2 = Textfield(d2)
A3 = Textfield(a3)
B3 = Textfield(b3)
D3 = Textfield(d3)
C3 = Textfield(c3)
text3: "⇒\left\lbrace \begin{array}{rr}" + a1 + " x" + (If[b1 < 0, "-", "+"]) + (abs(b1)) + "y" + (If[c1 < 0, "-", "+"]) + (abs(c1)) + "z=" + d1 + " \\ " + a2 + "x" + (If[b2 < 0, "-", "+"]) + (abs(b2)) + "y" + (If[c2 < 0, "-", "+"]) + (abs(c2)) + "z=" + d2 + " \\ " + a3 + "x" + (If[b3 < 0, "-", "+"]) + (abs(b3)) + "y" + (If[c3 < 0, "-", "+"]) + (abs(c3)) + "z=" + d3 + "  \\ \end{array} \right."
δ: a1 * b2 * c3 + b1 * c2 * a3 + c1 * a2 * b3 - c1 * b2 * a3 - c2 * b3 * a1 - c3 * b1 * a2
text4: "Δ=\left\vert \begin{array}{rr} " + (LaTeX[a1]) + " & " + (LaTeX[b1]) + " & " + (LaTeX[c1]) + " \\ " + (LaTeX[a2]) + " & " + (LaTeX[b2]) + " & " + (LaTeX[c2]) + "\\ " + (LaTeX[a3]) + " & " + (LaTeX[b3]) + " &" + (LaTeX[c3]) + "\\ \end{array} \right\vert=" + (LaTeX[δ]) + " "
δ_x: d1 * b2 * c3 + b1 * c2 * d3 + c1 * d2 * b3 - c1 * b2 * d3 - c2 * b3 * d1 - c3 * b1 * d2
text5: "Δ_x=\left\vert \begin{array}{rr} " + (LaTeX[d1]) + " & " + (LaTeX[b1]) + " & " + (LaTeX[c1]) + " \\ " + (LaTeX[d2]) + " &" + (LaTeX[b2]) + " & " + (LaTeX[c2]) + " \\ " + (LaTeX[d3]) + " & " + (LaTeX[b3]) + " & " + (LaTeX[c3]) + " \\ \end{array} \right\vert =" + (LaTeX[δ_x]) + ""
δ_y: a1 * d2 * c3 + d1 * c2 * a3 + c1 * a2 * d3 - c1 * d2 * a3 - c2 * d3 * a1 - c3 * d1 * a2
text6: "Δ_y=\left\vert \begin{array}{rr} " + (LaTeX[a1]) + " & " + (LaTeX[d1]) + " & " + (LaTeX[c1]) + " \\ " + (LaTeX[a2]) + " & " + (LaTeX[d2]) + " &" + (LaTeX[c2]) + " \\ " + (LaTeX[a3]) + " & " + (LaTeX[d3]) + "&" + (LaTeX[c3]) + "  \\ \end{array} \right\vert=" + (LaTeX[δ_y]) + " "
δ_z: a1 * b2 * d3 + b1 * d2 * a3 + d1 * a2 * b3 - d1 * b2 * a3 - d2 * b3 * a1 - d3 * b1 * a2
text7: "Δ_z=\left\vert\begin{array}{rr} " + (LaTeX[a1]) + " & " + (LaTeX[b1]) + " & " + (LaTeX[d1]) + " \\ " + (LaTeX[a2]) + "& " + (LaTeX[b2]) + " & " + (LaTeX[d2]) + "\\ " + (LaTeX[a3]) + " & " + (LaTeX[b3]) + " & " + (LaTeX[d3]) + " \\ \end{array}  \right\vert=" + (LaTeX[δ_z]) + " "
text8: "⇒x=\frac{" + (LaTeX[δ_x]) + " }{" + (LaTeX[δ]) + " }=" + (LaTeX[FractionText[δ_x / δ]]) + ""
text9: "y=\frac{" + δ_y + "}{" + δ + "}=" + (FractionText[δ_y / δ])
text10: "z=\frac{" + δ_z + "}{" + δ + "}=" + (FractionText[δ_z / δ])
A = (-3.3, -1)