行列式的性質(3)
Author: 藍邦偉  老師

\left|\begin{array}{cc} a & c+e \ b & d+f \ \end{array}\right|=\left|\begin{array}{cc} a & c \ b & d \ \end{array}\right|+\left|\begin{array}{} a & e \ b & f \ \end{array}\right|

四邊形OABC面積+四邊形CBDE面積

=四邊形OADE面積

\because{} \Delta OCE≅ \Delta ABD

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
A = (1.12, 2.8000000000000003)
C = (3.2, 1.62)
O = (0, 0)
B: A + C - O
a = Segment(O, C)
b = Segment(C, B)
c = Segment(B, A)
d = Segment(A, O)
e = 2.3 (slider from -5 to 5, step 0.1)
f = -0.2 (slider from -5 to 5, step 0.1)
E: (x(C) + e, y(C) + f)
D: A + E - O
g = Segment(C, E)
h = Segment(E, D)
i = Segment(D, B)
j = Segment(A, D)
k = Segment(O, E)
文字4: "|\left|\begin{array}{cc}" + (x(A)) + " & " + (x(C)) + " \\" + (y(A)) + " &" + (y(C)) + " \\ \end{array}\right||+|\left|\begin{array}{cc}" + (x(A)) + " &" + e + " \\" + (y(A)) + " &" + f + " \\ \end{array}\right||"
文字6: "=|\left|\begin{array}{cc}" + (LaTeX[x(A)]) + " & " + (LaTeX[x(E)]) + " \\" + (LaTeX[y(A)]) + " &" + (LaTeX[y(E)]) + " \\ \end{array}\right||"
text1: "A" + (LaTeX[A]) + ""
text2: "E" + E
text3: "C" + C