矩陣的乘法
Author: 藍邦偉  老師

$隨機值%v$

矩陣的乘法

$情況%v$

$ a_{11}\;\;a_{12}\;\;a_{13} $

$ a_{21}\;\;a_{22}\;\;a_{23} $

$ a_{31}\;\;a_{32}\;\;a_{33} $

$ b_{11} $
$b_{21}$
$b_{31}$

$ b_{12} $
$b_{22}$
$b_{32}$

$ b_{13} $
$b_{23}$
$b_{33}$

$ = $

$ c_{11}=a_{11}×b_{11}+a_{12}×b_{21}+a_{13}×b_{31} $

$ c_{12} $

$ c_{13} $

$ c_{21} $

$ c_{22} $

$ c_{23} $

$ c_{31} $

$ c_{32} $

c_{23}

$ c_{12}=a_{11}×b_{12}+a_{12}×b_{22}+a_{13}×b_{32} $

$ c_{13}=a_{11}×b_{13}+a_{12}×b_{23}+a_{13}×b_{33} $

$ c_{21}=a_{21}×b_{11}+a_{22}×b_{21}+a_{23}×b_{31} $

$  c_{22}=a_{21}×b_{12}+a_{22}×b_{22}+a_{23}×b_{32}$

$ c_{23}=a_{21}×b_{13}+a_{22}×b_{23}+a_{23}×b_{33} $

$ c_{31}=a_{31}×b_{11}+a_{32}×b_{21}+a_{33}×b_{31} $

$ c_{32}=a_{31}×b_{12}+a_{32}×b_{22}+a_{33}×b_{32} $

$ c_{33}=a_{31}×b_{13}+a_{32}×b_{23}+a_{33}×b_{33} $

$觀察%v$

c_{11}

$ 結論 ：$

s = 1 (slider from 0 to 1, step 0.1)
L2 = Sequence(Random[-5, 4] + s * 0, i, 1, 20)
L1 = Sequence(If[Element[L2, i] ≟ 0, 5, Element[L2, i]], i, 1, 18)
a_{11} = Element(L1, 1)
a_{12} = Element(L1, 2)
a_{21} = Element(L1, 4)
a_{22} = Element(L1, 5)
a_{31} = Element(L1, 7)
a_{32} = Element(L1, 8)
b_{11} = Element(L1, 10)
b_{12} = Element(L1, 11)
b_{13} = Element(L1, 12)
b_{22} = Element(L1, 14)
b_{21} = Element(L1, 13)
b_{23} = Element(L1, 15)
n = 0 (slider from 0 to 10, step 1)
a_{13} = Element(L1, 3)
a_{23} = Element(L1, 6)
a_{33} = Element(L1, 9)
b_{31} = Element(L1, 16)
b_{32} = Element(L1, 17)
b_{33} = Element(L1, 18)
A = (-0.7, 6.68)
text5: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " & " + (LaTeX[a_{13}]) + " \end{array}  \right ] \cdot \left [  \begin{array}{cc} " + (LaTeX[b_{11}]) + " \\ " + (LaTeX[b_{21}]) + " \\ " + (LaTeX[b_{31}]) + " \end{array} \right ] =\left [  " + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21} + a_{13} * b_{31}]) + "\right ]  $"
text6: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " \\ " + (LaTeX[a_{21}]) + " \\ " + (LaTeX[a_{31}]) + " \end{array}  \right ]\cdot  \left [ \begin{array}{cc} " + (LaTeX[b_{11}]) + " & " + (LaTeX[b_{12}]) + " & " + (LaTeX[b_{13}]) + " \end{array}  \right ] =\left [\begin{array}{cc} " + (LaTeX[a_{11} * b_{11}]) + " & " + (LaTeX[a_{11} * b_{12}]) + " & " + (LaTeX[a_{11} * b_{13}]) + " \\ " + (LaTeX[a_{21} * b_{11}]) + " & " + (LaTeX[a_{21} * b_{12}]) + " & " + (LaTeX[a_{21} * b_{13}]) + " \\ " + (LaTeX[a_{31} * b_{11}]) + " & " + (LaTeX[a_{31} * b_{12}]) + " &" + (LaTeX[a_{31} * b_{13}]) + " \\ \end{array}  \right ]  $"
text1: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " \end{array}  \right ]\cdot \left [  \begin{array}{cc} " + (LaTeX[b_{11}]) + " \\ " + (LaTeX[b_{21}]) + " \end{array} \right ] =[" + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21}]) + "]  $"
text3: "$ \left [\begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " \end{array}   \right ] \cdot \left [\begin{array}{cc} " + (LaTeX[b_{11}]) + "& " + (LaTeX[b_{12}]) + " \\ " + (LaTeX[b_{21}]) + " & " + (LaTeX[b_{22}]) + " \\ \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}]) + " \end{array}  \right ]  $"
text4: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " \\ " + (LaTeX[a_{21}]) + " & " + (LaTeX[a_{22}]) + " \\ \end{array}  \right ]\cdot \left [ \begin{array}{cc} " + (LaTeX[b_{11}]) + " \\ " + (LaTeX[b_{21}]) + "  \end{array}  \right ]  =\left [ \begin{array}{cc} " + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21}]) + " \\" + (LaTeX[a_{21} * b_{11} + a_{22} * b_{21}]) + "  \end{array}  \right ]  $"
text7: "$ \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 ] \cdot \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 ]   $"
text9: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " &" + (LaTeX[a_{13}]) + " \\ " + (LaTeX[a_{21}]) + "& " + (LaTeX[a_{22}]) + " &" + (LaTeX[a_{23}]) + "\\ " + (LaTeX[a_{31}]) + "& " + (LaTeX[a_{32}]) + " &" + (LaTeX[a_{33}]) + " \\ \end{array} \right ]\cdot   \left [  \begin{array}{cc} " + (LaTeX[b_{11}]) + " & " + (LaTeX[b_{12}]) + " & " + (LaTeX[b_{13}]) + " \\ " + (LaTeX[b_{21}]) + " & " + (LaTeX[b_{22}]) + " &" + (LaTeX[b_{23}]) + " \\ " + (LaTeX[b_{31}]) + " & " + (LaTeX[b_{32}]) + " & " + (LaTeX[b_{33}]) + " \\ \end{array}\right ] $
$=\left [  \begin{array}{cc} " + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21} + a_{13} * b_{31}]) + " & " + (LaTeX[a_{11} * b_{12} + a_{12} * b_{22} + a_{13} * b_{32}]) + " & " + (LaTeX[a_{11} * b_{13} + a_{12} * b_{23} + a_{13} * b_{33}]) + " \\ " + (LaTeX[a_{21} * b_{11} + a_{22} * b_{21} + a_{23} * b_{31}]) + " & " + (LaTeX[a_{21} * b_{12} + a_{22} * b_{22} + a_{23} * b_{32}]) + " & " + (LaTeX[a_{21} * b_{13} + a_{22} * b_{23} + a_{23} * b_{33}]) + " \\ " + (LaTeX[a_{31} * b_{11} + a_{32} * b_{21} + a_{33} * b_{31}]) + "& " + (LaTeX[a_{31} * b_{12} + a_{32} * b_{22} + a_{33} * b_{32}]) + " & " + (LaTeX[a_{31} * b_{13} + a_{32} * b_{23} + a_{33} * b_{33}]) + " \\ \end{array}\right ] $"
text8: "$ \left [ \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + (LaTeX[a_{12}]) + " & " + (LaTeX[a_{13}]) + " \\ " + (LaTeX[a_{21}]) + " & " + (LaTeX[a_{22}]) + " & " + (LaTeX[a_{23}]) + " \\ \end{array} \right ] \cdot \left [  \begin{array}{cc} " + (LaTeX[b_{11}]) + " &" + (LaTeX[b_{12}]) + "  \\ " + (LaTeX[b_{21}]) + "& " + (LaTeX[b_{22}]) + "  \\ " + (LaTeX[b_{31}]) + " & " + (LaTeX[b_{32}]) + "  \\ \end{array}\right ] =\left [ \begin{array}{cc} " + (LaTeX[a_{11} * b_{11} + a_{12} * b_{21} + a_{13} * b_{31}]) + " & " + (LaTeX[a_{11} * b_{12} + a_{12} * b_{22} + a_{13} * b_{32}]) + " \\ " + (LaTeX[a_{21} * b_{11} + a_{22} * b_{21} + a_{23} * b_{31}]) + " & " + (LaTeX[a_{21} * b_{12} + a_{22} * b_{22} + a_{23} * b_{32}]) + " \\ \end{array}  \right ]  $"
text2: "$ \left [\begin{array}{cc} " + (LaTeX[a_{11}]) + " \\ " + (LaTeX[a_{21}]) + " \end{array}   \right ]\cdot \left [\begin{array}{cc} " + (LaTeX[b_{11}]) + " & " + (LaTeX[b_{12}]) + "  \end{array}  \right ] =\left [ \begin{array}{cc} " + (LaTeX[a_{11} * b_{11}]) + " & " + (LaTeX[a_{11} * b_{12}]) + " \\ " + (LaTeX[a_{21} * b_{11}]) + " & " + (LaTeX[a_{21} * b_{12}]) + " \\ \end{array}  \right ]   $"
B = (-0.18, 3.74)
k = 0 (slider from 0 to 9, step 1)
C: B - (-1, 1.3)
a = If(n ≟ 10, 0)
b = If(n ≟ 10, 0)
c = If(n ≟ 10, 0)
d = If(n ≟ 10, 0)
e = If(n ≟ 10, 0)
f = If(n ≟ 10, 0)
g = If(n ≟ 10, 0)
h = If(n ≟ 10, 0)
i = If(n ≟ 10, 0)
j = If(n ≟ 10, 0)
l = If(n ≟ 10, 0)
m = If(n ≟ 10, 0)
o = If(n ≟ 10, 0)
p = If(n ≟ 10, 0)
q = If(n ≟ 10, 0)
r = If(n ≟ 10, 0)
t = If(n ≟ 10, 0)
u = If(n ≟ 10, 0)
v = If(n ≟ 10, 0)
w = If(n ≟ 10, 0)
z = If(n ≟ 10, 0)