二階反方陣
Author: 藍邦偉  老師

二階反方陣

A=\left[\begin{array}{cc} a & b \ c & d \ \end{array}\right]^-^^1= \frac{ 1 }{\left|\begin{array}{cc} a & b \ c & d \ \end{array}\right| } \left[\begin{array}{cc} d & -b \ -c & a \ \end{array}\right]

A\cdot{}A^-^1=A^-^1\cdot{}A=I

u = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
v = Vector((0.0, y(Corner[1.0])), (0.0, y(Corner[3.0])))
s = 1.8 (slider from 0 to 5, step 0.1)
L1 = Sequence(Random[-5.0, 5.0] + s * 0.0, i, 1.0, 20.0)
a_{11} = Element(L1, 1.0)
a_{12} = Element(L1, 2.0)
a_{21} = Element(L1, 3.0)
a_{22} = Element(L1, 4.0)
a_{31} = Element(L1, 5.0)
a_{32} = Element(L1, 6.0)
b_{11} = Element(L1, 7.0)
b_{12} = Element(L1, 8.0)
b_{13} = Element(L1, 9.0)
b_{114} = Element(L1, 10.0)
b_{22} = Element(L1, 11.0)
b_{21} = Element(L1, 10.0)
b_{23} = Element(L1, 12.0)
D: a_{11} * a_{22} - a_{12} * a_{21}
文字3: "" + (If[D ≟ 0.0, "因為det(A)=\left|\begin{array}{cc}" + a_{11} + "&" + a_{12} + "  \\ " + a_{21} + " &" + a_{22} + " \\ \end{array}\right|=0,所以A反矩陣不存在", "A^{-1}=\left[\begin{array}{cc}" + a_{11} + "&" + a_{12} + "  \\ " + a_{21} + " &" + a_{22} + " \\ \end{array}\right]=\frac{1 }{" + D + " } \left[\begin{array}{cc}" + a_{22} + " &" + (-(a_{12})) + " \\" + (-(a_{21})) + " & " + a_{11} + " \\ \end{array}\right]=\left[\begin{array}{cc} " + (FractionText[a_{22} / D]) + " &" + (FractionText[-(a_{12}) / D]) + " \\" + (FractionText[-(a_{21}) / D]) + "&" + (FractionText[a_{11} / D]) + " \\ \end{array}\right]"])