矩陣的乘法
Author: 藍邦偉  老師

矩陣的乘法

\left[\begin{array}{cc} a & b \ c & d \e&f\ \end{array}\right]\left[\begin{array}{cc} p & q&r \  x& y&z \ \end{array}\right]=\left[\begin{array}{cc} ap+bx & aq+by & ar+bz \ cp+dx & cq+dy & cr+dz \ ep+fx & eq+fy & er+fz \ \end{array}\right]

\left[\begin{array}{cc} a & b &c\ d & e&f \ \end{array}\right]\left[\begin{array}{cc} p & q  \ s & t \ u & v \ \end{array}\right]=\left[\begin{array}{cc} ap+bs+cu & aq+bt+cv \ dp+es+fu & dq+et+fd \ \end{array}\right] 

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
s = 0.7 (slider from 0 to 1, step 0.1)
L1 = Sequence(Random[-5, 5] + s * 0, i, 1, 20)
a_{11} = Element(L1, 1)
a_{12} = Element(L1, 2)
a_{21} = Element(L1, 3)
a_{22} = Element(L1, 4)
a_{31} = Element(L1, 5)
a_{32} = Element(L1, 6)
b_{11} = Element(L1, 7)
b_{12} = Element(L1, 8)
b_{13} = Element(L1, 9)
b_{114} = Element(L1, 10)
b_{22} = Element(L1, 11)
b_{21} = Element(L1, 10)
b_{23} = Element(L1, 12)
n = 0 (slider from 0 to 6, step 1)
文字10: "\left[\begin{array}{cc} " + a_{11} + " &" + a_{12} + " \\  \\ \end{array}\right]\cdot{}\left[\begin{array}{}" + b_{11} + " \\" + b_{21} + "\\ \end{array}\right]=[" + (a_{11} * b_{11} + a_{12} * b_{21}) + "]"
文字12: "\left[\begin{array}{cc}" + a_{11} + " &" + a_{12} + " \\ \end{array}\right]\cdot{}\left[\begin{array}{cc}" + b_{11} + " &" + b_{12} + " \\" + b_{21} + " &" + b_{22} + " \\ \end{array}\right]=\left[\begin{array}{cc}" + (a_{11} * b_{11} + a_{12} * b_{21}) + " &" + (a_{11} * b_{12} + a_{12} * b_{22}) + " \\ \end{array}\right]"
文字11: "\left[\begin{array}{cc}" + a_{11} + " &" + a_{12} + "\\ " + a_{21} + "&" + a_{22} + "\\ \end{array}\right]\cdot{}\left[\begin{array}{cc}" + b_{11} + " \\" + b_{21} + " \\ \end{array}\right]=\left[\begin{array}{cc}" + (a_{11} * b_{11} + a_{12} * b_{21}) + " \\" + (a_{21} * b_{11} + a_{22} * b_{21}) + " \\ \end{array}\right]"
文字13: "\left[\begin{array}{cc} " + a_{11} + " \\" + a_{21} + " \\ \end{array}\right]\cdot{}\left[\begin{array}{cc}" + b_{11} + " &" + b_{12} + "\\ \end{array}\right]=\left[\begin{array}{cc}" + (a_{11} * b_{11}) + " &" + (a_{11} * b_{12}) + " \\" + (a_{21} * b_{11}) + " &" + (a_{21} * b_{12}) + " \\ \end{array}\right]"
文字6: "\left[\begin{array}{cc} " + (LaTeX[b_{11}]) + " &" + (LaTeX[b_{12}]) + " & " + (LaTeX[b_{13}]) + " \\ " + (LaTeX[b_{21}]) + "& " + (LaTeX[b_{22}]) + " & " + (LaTeX[b_{23}]) + "  \\ \end{array}\right]\left[\begin{array}{cc} " + (LaTeX[a_{11}]) + "& " + (LaTeX[a_{12}]) + "  \\  " + (LaTeX[a_{21}]) + " & " + (LaTeX[a_{22}]) + " \\" + (LaTeX[a_{31}]) + "  &" + (LaTeX[a_{32}]) + "   \\ \end{array}\right]=\left[\begin{array}{cc} " + (LaTeX[b_{11} * a_{11} + b_{12} * a_{21} + b_{13} * a_{31}]) + "  &" + (LaTeX[b_{11} * a_{12} + b_{12} * a_{22} + b_{13} * a_{32}]) + "  \\ " + (LaTeX[b_{21} * a_{11} + b_{22} * a_{21} + b_{23} * a_{31}]) + " &" + (LaTeX[b_{21} * a_{12} + b_{22} * a_{22} + b_{23} * a_{32}]) + "  \\ \end{array}\right]"
文字4: "\left[\begin{array}{cc}" + (LaTeX[a_{11}]) + "&" + (LaTeX[a_{12}]) + "  \\ " + (LaTeX[a_{21}]) + " &" + (LaTeX[a_{22}]) + " \\" + (LaTeX[a_{31}]) + " &" + (LaTeX[a_{32}]) + "  \\ \end{array}\right]\left[\begin{array}{cc}" + (LaTeX[b_{11}]) + "  &" + (LaTeX[b_{12}]) + "  &" + (LaTeX[b_{13}]) + "   \\" + (LaTeX[b_{21}]) + "  &" + (LaTeX[b_{22}]) + "   & " + (LaTeX[b_{23}]) + "   \\ \end{array}\right]
=\left[\begin{array}{cc}" + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21}]) + " &" + (LaTeX[a_{11} * b_{12} + a_{12} * b_{22}]) + "  &" + (LaTeX[a_{11} * b_{13} + a_{12} * b_{23}]) + "  \\ " + (LaTeX[a_{21} * b_{11} + a_{22} * b_{21}]) + "  &" + (LaTeX[a_{21} * b_{12} + a_{22} * b_{22}]) + "  &" + (LaTeX[a_{21} * b_{13} + a_{22} * b_{23}]) + "  \\ " + (LaTeX[a_{31} * b_{11} + a_{32} * b_{21}]) + "  &" + (LaTeX[a_{31} * b_{12} + a_{32} * b_{22}]) + "  &" + (LaTeX[a_{31} * b_{13} + a_{32} * b_{23}]) + "  \\ \end{array}\right]"