克拉瑪公式與其幾何意義
Author: 藍邦偉  老師

二階克拉瑪公式

a_1

a_1=

b_1=

b_1

c_1=

c_1

a_2=

a_2

b_2=

b_2

c_2=

c_2

a_1 = 2 (slider from -5 to 5, step 1)
b_1 = -3 (slider from -5 to 5, step 1)
c_1 = -5 (slider from -5 to 5, step 1)
a_2 = 3 (slider from -5 to 5, step 1)
b_2 = 2 (slider from -5 to 5, step 1)
c_2 = -2 (slider from -5 to 5, step 1)
文字7: "Δ_x=\left|\begin{array}{rr}" + c_1 + " &" + b_1 + " \\" + c_2 + " &" + b_2 + " \\ \end{array}\right|=" + (c_1 * b_2 - c_2 * b_1)
文字5: "Δ_y=\left|\begin{array}{rr}" + a_1 + " &" + c_1 + " \\" + a_2 + " &" + c_2 + " \\ \end{array}\right|=" + (a_1 * c_2 - a_2 * c_1)
文字1: "x= \frac{ " + (c_1 * b_2 - c_2 * b_1) + " }{ " + (a_1 * b_2 - a_2 * b_1) + "} =" + (FractionText[(c_1 * b_2 - c_2 * b_1) / (a_1 * b_2 - a_2 * b_1)])
文字2: "y= \frac{ " + (a_1 * c_2 - a_2 * c_1) + " }{ " + (a_1 * b_2 - a_2 * b_1) + "} =" + (FractionText[(a_1 * c_2 - a_2 * c_1) / (a_1 * b_2 - a_2 * b_1)])
P_1 = Corner(1)
P_4 = Corner(4)
P_2: (7 * Corner[1] + 3 * Corner[2]) / 10
P_3: (7 * Corner[4] + 3 * Corner[3]) / 10
多邊形1, p_1, p_2, p_3, p_4 = Polygon(P_1, P_2, P_3, P_4)
a = Segment(P_2, P_3)
L_1: a_1 * x + b_1 * y = c_1
L_2: a_2 * x + b_2 * y = c_2
A = Intersect(L_1, L_2)
Q_1: (x(Corner[1]), 0)
Q_2: (x(Corner[2]), 0)
Q_3: (0, y(Corner[2]))
Q_4: (0, y(Corner[3]))
u = Vector(Q_1, Q_2)
v = Vector(Q_3, Q_4)
文字4: "Δ=\left|\begin{array}{rr} " + a_1 + " &" + b_1 + " \\" + a_2 + " &" + b_2 + " \\ \end{array}\right|=" + (a_1 * b_2 - a_2 * b_1)
inputBox1 = Textfield(a_1)
inputBox2 = Textfield(b_1)
inputBox3 = Textfield(c_1)
inputBox4 = Textfield(a_2)
inputBox5 = Textfield(b_2)
inputBox6 = Textfield(c_2)
text7: " \left\lbrace  \begin{array}{} " + a_1 + "x" + (If[b_1 < 0, "-", "+"]) + (abs(b_1)) + "y" + "=" + c_1 + "\\" + a_2 + "x" + (If[b_2 < 0, "-", "+"]) + (abs(b_2)) + "y" + "=" + c_2 + " \\ \end{array} \right."