行列式的性質(2)
Author: 藍邦偉  老師

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\left|\begin{array}{cc} ka & b \ kc & d \ \end{array}\right|=k\left|\begin{array}{} a & b \ c & d \ \end{array}\right|

四邊形OABC的面積為

|k| h

四邊形OA'B'C的面積為

Reset

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
A = (2, 4)
C = (4, 2)
O = (0, 0)
B: A + C - O
a = Segment(O, A)
b = Segment(A, B)
c = Segment(B, C)
d = Segment(C, O)
e = OrthogonalLine(A, d)
f = true
g = false
k = -0.5 (slider from -5 to 5, step 0.1)
A': abs(k) * A
B': A' + C - O
i = Segment(O, A')
j = Segment(A', B')
l = Segment(B', C)
m = OrthogonalLine(A', d)
A_1 = Area(O, C, A, B)
a_1 = Area(O, A, B, C)
n = Line(O, C)
p = OrthogonalLine(A', n)
D = Intersect(p, n)
H = Intersect(e, n)
h = Segment(A, H)
q = Segment(A', D)
文字2: "\overrightarrow{OA}=\left[\begin{array}{} " + (LaTeX[x(A)]) + "  \\" + (LaTeX[y(A)]) + " \\ \end{array}\right]"
文字3: "\overrightarrow{OC}=\left[\begin{array}{} " + (LaTeX[x(C)]) + "  \\" + (LaTeX[y(C)]) + " \\ \end{array}\right]"
文字5: "|\left|\begin{array}{} " + (LaTeX[x(A)]) + " &" + (LaTeX[y(A)]) + " \\" + (LaTeX[x(C)]) + " &" + (LaTeX[y(C)]) + " \\ \end{array}\right||=" + (LaTeX[a_1]) + ""
文字6: "\overrightarrow{OA'}=\left[\begin{array}{ll} |" + (LaTeX[abs(k)]) + "|\times{}" + (LaTeX[x(A)]) + "  \\|" + (LaTeX[abs(k)]) + "|\times{}" + (LaTeX[y(A)]) + " \\ \end{array}\right]"
文字8: "|\left|\begin{array}{cc}| " + (LaTeX[abs(k)]) + "|\times{}" + (LaTeX[x(A)]) + " &|" + (LaTeX[abs(k)]) + "|\times{}" + (LaTeX[y(A)]) + " \\" + (LaTeX[x(C)]) + " &" + (LaTeX[y(C)]) + " \\ \end{array}\right||=|" + (LaTeX[abs(k)]) + "|\times{}" + (LaTeX[a_1]) + ""