二階反方陣(4.0版)
Author: 藍邦偉  老師

二階反方陣

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

a=

b=

c=

d=

AA^{-1}=A^{-1}A=I

A=\left [ \begin{array}{} a & b \ c & d \ \end{array}  \right ] 

a=

b=

c=

d=

s = 2 (slider from 0 to 5, step 0.1)
L1 = Sequence(Random[-5, 5] + s * 0, i, 1, 20)
a_{11} = 1
a_{22} = 3
a_{21} = 1
a_{12} = 2
a_{31} = Element(L1, 5)
a_{32} = Element(L1, 6)
b_{11} = Element(L1, 7)
b_{12} = Element(L1, 8)
b_{13} = Element(L1, 9)
b_{114} = Element(L1, 10)
b_{22} = Element(L1, 11)
b_{21} = Element(L1, 10)
b_{23} = Element(L1, 12)
D: a_{11} * a_{22} - a_{12} * a_{21}
inputBox1 = Textfield(a_{11})
inputBox2 = Textfield(a_{12})
inputBox3 = Textfield(a_{21})
inputBox4 = Textfield(a_{22})
text2: "A=\left [ \begin{array}{}" + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " \\ " + (LaTeX[a_{21}]) + " &" + (LaTeX[a_{22}]) + " \\ \end{array}  \right ] "
文字3: "" + (LaTeX[If[D ≟ 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]"]]) + ""