三階反方陣
Author: 藍邦偉　老師

a_{11}=

a_{12}=

a_{13}=

a_{21}=

a_{22}=

a_{23}=

a_{31}=

a_{32}=

a_{33}=

a11

a12

a13

a21

a22

a23

a31

a32

a33

1. 先求A的行列式值

2. 將A矩陣寫四次

$ 3. 把外圈元素扣除 $

$ 4. 整理成9個二階行列式 $

$ 5. 求出行列式值 $

$ 6. 轉置矩陣 $

$ 7. 把該矩陣同除det(A) $

a_1 = 4
a_2 = -1
a_3 = 3
b_1 = -2
b_2 = -5
b_3 = 4
c_1 = -3
c_2 = -1
c_3 = 5
Question: "A=\left [ \begin{array}{cc} " + (LaTeX[a_1]) + " & " + (LaTeX[a_2]) + " & " + (LaTeX[a_3]) + " \\ " + (LaTeX[b_1]) + " & " + (LaTeX[b_2]) + " & " + (LaTeX[b_3]) + " \\ " + (LaTeX[c_1]) + " & " + (LaTeX[c_2]) + " & " + (LaTeX[c_3]) + " \\ \end{array} \right ] ,A^{-1}=?"
T2: "⇒\left [ \begin{array}{cc} " + (LaTeX[a_1]) + " & " + (LaTeX[a_2]) + " & " + (LaTeX[a_3]) + "&" + (LaTeX[a_1]) + "&" + (LaTeX[a_2]) + "&" + (LaTeX[a_3]) + " \\ " + (LaTeX[b_1]) + " & " + (LaTeX[b_2]) + " & " + (LaTeX[b_3]) + " &" + (LaTeX[b_1]) + "&" + (LaTeX[b_2]) + "&" + (LaTeX[b_3]) + "\\ " + (LaTeX[c_1]) + " & " + (LaTeX[c_2]) + " &" + (LaTeX[c_3]) + "&" + (LaTeX[c_1]) + "&" + (LaTeX[c_2]) + "&" + (LaTeX[c_3]) + "\\" + (LaTeX[a_1]) + "&" + (LaTeX[a_2]) + "&" + (LaTeX[a_3]) + "&" + (LaTeX[a_1]) + "&" + (LaTeX[a_2]) + "&" + (LaTeX[a_3]) + "\\" + (LaTeX[b_1]) + "&" + (LaTeX[b_2]) + "&" + (LaTeX[b_3]) + "&" + (LaTeX[b_1]) + "&" + (LaTeX[b_2]) + "&" + (LaTeX[b_3]) + "\\" + (LaTeX[c_1]) + "&" + (LaTeX[c_2]) + "&" + (LaTeX[c_3]) + "&" + (LaTeX[c_1]) + "&" + (LaTeX[c_2]) + "& " + (LaTeX[c_3]) + "\\ \end{array} \right ] "
T3: "⇒\left [  \begin{array}{cc}  " + (LaTeX[b_2]) + "& " + (LaTeX[b_3]) + "&" + (LaTeX[b_1]) + " &" + (LaTeX[b_2]) + " \\  " + (LaTeX[c_2]) + "& " + (LaTeX[c_3]) + " &" + (LaTeX[c_1]) + " &" + (LaTeX[c_2]) + " \\  " + (LaTeX[a_2]) + "&" + (LaTeX[a_3]) + "  &" + (LaTeX[a_1]) + "&" + (LaTeX[a_2]) + " \\" + (LaTeX[b_2]) + "&" + (LaTeX[b_3]) + "&" + (LaTeX[b_1]) + "&" + (LaTeX[b_2]) + " \end{array}\right ] "
T5: "$ ⇒\left [ \begin{array}{cc} " + (LaTeX[b_2 * c_3 - b_3 * c_2]) + " & " + (LaTeX[b_3 * c_1 - b_1 * c_3]) + " & " + (LaTeX[b_1 * c_2 - b_2 * c_1]) + " \\ " + (LaTeX[c_2 * a_3 - c_3 * a_2]) + " & " + (LaTeX[c_3 * a_1 - c_1 * a_3]) + " & " + (LaTeX[c_1 * a_2 - c_2 * a_1]) + " \\ " + (LaTeX[a_2 * b_3 - a_3 * b_2]) + " & " + (LaTeX[a_3 * b_1 - a_1 * b_3]) + " & " + (LaTeX[a_1 * b_2 - a_2 * b_1]) + " \\ \end{array} \right ]  $"
D: a_1 * b_2 * c_3 + a_2 * b_3 * c_1 + a_3 * b_1 * c_2 - a_3 * b_2 * c_1 - b_3 * c_2 * a_1 - c_3 * a_2 * b_1
T6: "⇒\left [\begin{array}{cc} " + (LaTeX[b_2 * c_3 - b_3 * c_2]) + " & " + (LaTeX[c_2 * a_3 - c_3 * a_2]) + " & " + (LaTeX[a_2 * b_3 - a_3 * b_2]) + " \\ " + (LaTeX[b_3 * c_1 - b_1 * c_3]) + " & " + (LaTeX[c_3 * a_1 - c_1 * a_3]) + " & " + (LaTeX[a_3 * b_1 - a_1 * b_3]) + " \\ " + (LaTeX[b_1 * c_2 - b_2 * c_1]) + " & " + (LaTeX[c_1 * a_2 - c_2 * a_1]) + " &" + (LaTeX[a_1 * b_2 - a_2 * b_1]) + " \\ \end{array}  \right ] "
Answer: "⇒A^{-1}=\left [\begin{array}{cc} " + (LaTeX[FractionText[(c_3 * b_2 - c_2 * b_3) / D]]) + " & " + (LaTeX[FractionText[(c_2 * a_3 - c_3 * a_2) / D]]) + " & " + (LaTeX[FractionText[(a_2 * b_3 - a_3 * b_2) / D]]) + " \\ " + (LaTeX[FractionText[(b_3 * c_1 - b_1 * c_3) / D]]) + " & " + (LaTeX[FractionText[(a_1 * c_3 - a_3 * c_1) / D]]) + " & " + (LaTeX[FractionText[(a_3 * b_1 - a_1 * b_3) / D]]) + " \\ " + (LaTeX[FractionText[(b_1 * c_2 - b_2 * c_1) / D]]) + " & " + (LaTeX[FractionText[(a_2 * c_1 - a_1 * c_2) / D]]) + " & " + (LaTeX[FractionText[(a_1 * b_2 - a_2 * b_1) / D]]) + " \\ \end{array}  \right ] "
T4: "⇒\left [\begin{array}{cc} \left\vert \begin{array}{cc} " + (LaTeX[b_2]) + " & " + (LaTeX[b_3]) + " \\ " + (LaTeX[c_2]) + " & " + (LaTeX[c_3]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[b_3]) + " & " + (LaTeX[b_1]) + " \\ " + (LaTeX[c_3]) + " & " + (LaTeX[c_1]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[b_1]) + " & " + (LaTeX[b_2]) + " \\ " + (LaTeX[c_1]) + " & " + (LaTeX[c_2]) + " \\ \end{array}  \right\vert  \\ \left\vert \begin{array}{cc} " + (LaTeX[c_2]) + " & " + (LaTeX[c_3]) + " \\ " + (LaTeX[a_2]) + " & " + (LaTeX[a_3]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[c_3]) + " & " + (LaTeX[c_1]) + " \\ " + (LaTeX[a_3]) + " & " + (LaTeX[a_1]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[c_1]) + " & " + (LaTeX[c_2]) + " \\ " + (LaTeX[a_1]) + " & " + (LaTeX[a_2]) + " \\ \end{array}  \right\vert  \\ \left\vert \begin{array}{cc} " + (LaTeX[a_2]) + " & " + (LaTeX[a_3]) + " \\ " + (LaTeX[b_2]) + " & " + (LaTeX[b_3]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[a_3]) + " & " + (LaTeX[a_1]) + " \\ " + (LaTeX[b_3]) + " & " + (LaTeX[b_1]) + " \\ \end{array}  \right\vert  & \left\vert \begin{array}{cc} " + (LaTeX[a_1]) + " & " + (LaTeX[a_2]) + " \\ " + (LaTeX[b_1]) + " & " + (LaTeX[b_2]) + " \\ \end{array}  \right\vert  \\ \end{array}  \right ] "
T1: "\left\vert \begin{array}{cc} " + (LaTeX[a_1]) + " & " + (LaTeX[a_2]) + " & " + (LaTeX[a_3]) + " \\ " + (LaTeX[b_1]) + " & " + (LaTeX[b_2]) + " &" + (LaTeX[b_3]) + " \\ " + (LaTeX[c_1]) + " & " + (LaTeX[c_2]) + " & " + (LaTeX[c_3]) + " \\ \end{array} \right\vert =" + (LaTeX[D]) + "" + (LaTeX[If[D ≟ 0, ",反方陣不存在", ""]]) + ""
inputBox1 = Textfield(a_1)
inputBox2 = Textfield(a_2)
inputBox3 = Textfield(a_3)
inputBox4 = Textfield(b_1)
inputBox5 = Textfield(b_2)
inputBox6 = Textfield(b_3)
inputBox7 = Textfield(c_1)
inputBox8 = Textfield(c_2)
inputBox9 = Textfield(c_3)
A = (-4.02, 4.3)
B_4 = (-2.58, -0.52)
B_1: B_4 + (0, -1.75)
B_2: B_1 + (2.9, 0)
B_3: (x(B_2), y(B_4))
poly1, b_5, b_6, b_7, b_4 = Polygon(B_1, B_2, B_3, B_4)
s = 0 (slider from 0 to 8, step 1)
B = (1.2, 4.88)