行列式的性質(1)
Author: 藍邦偉  老師

行列互換其值不變

行列互換其值不變

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

兩行互換

兩列互換

y=x

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
P = (4, 2)
Q = (2, 6)
O = (0, 0)
a = Segment(Q, O)
b = Segment(O, P)
c = Segment(P, Q)
d = true
e = false
P' = Mirror(P, L)
Q' = Mirror(Q, L)
f = Segment(P', O)
g = Segment(O, Q')
h = Segment(Q', P')
a_1 = Area(O, P, Q)
文字3: "\Delta OPQ= \frac{ 1 }{2 } |\left|\begin{array}{cc} " + (LaTeX[x(P)]) + " &" + (LaTeX[y(P)]) + " \\ " + (LaTeX[x(Q)]) + "&" + (LaTeX[y(Q)]) + " \\ \end{array}\right||=" + (LaTeX[a_1]) + ""
文字5: "\Delta OQ'P'= \frac{ 1 }{2 } |\left|\begin{array}{cc} " + (LaTeX[x(Q)]) + " &" + (LaTeX[x(P)]) + " \\ " + (LaTeX[y(Q)]) + "&" + (LaTeX[y(P)]) + " \\ \end{array}\right||=" + (LaTeX[a_1]) + ""
文字4: "\Delta OPQ= \frac{ 1 }{2 } |\left|\begin{array}{cc} " + (LaTeX[y(P)]) + " &" + (LaTeX[y(Q)]) + " \\ " + (LaTeX[x(P)]) + "&" + (LaTeX[x(Q)]) + " \\ \end{array}\right||=" + (LaTeX[a_1]) + ""