# Matrices 3D

### Definición:

La multiplicación se define como:

\begin{equation}
(AB)C
\end{equation}

**Ejemplo 1**:Multiplicar:

\begin{equation}
\left [
\begin{matrix}
1 \\\
2 \\\
3
\end{matrix}
\right ]
\left [
\begin{matrix}
4 & 5 & 6
\end{matrix}
\right ]
\left [
\begin{matrix}
7 & 8 & 9
\end{matrix}
\right ]
\end{equation}

Primero se multiplican $A$ y $B$:

\begin{equation}
\left [
\begin{matrix}
1 \\\
2 \\\
3
\end{matrix}
\right ]
\left [
\begin{matrix}
4 & 5 & 6
\end{matrix}
\right ] = \left [
\begin{matrix}
4 & 5 & 6 \\\
8 & 10 & 12 \\\
12 & 15 & 18
\end{matrix}
\right ]
\end{equation}

Luego se multiplican todas las columnas de $AB$ con $C$.

\begin{equation}
\left [
\begin{matrix}
4 \\\
8 \\\
12
\end{matrix}
\right ]
\left [
\begin{matrix}
7 & 8 & 9
\end{matrix}
\right ] = \left [
\begin{matrix}
28 & 32 & 36 \\\
56 & 64 & 72 \\\
84 & 96 & 108
\end{matrix}
\right ]
\end{equation}
      
\begin{equation}
\left [
\begin{matrix}
5 \\\
10 \\\
15
\end{matrix}
\right ]
\left [
\begin{matrix}
7 & 8 & 9
\end{matrix}
\right ] = \left [
\begin{matrix}
35 & 40 & 45 \\\
70 & 80 & 90 \\\
105 & 120 & 135
\end{matrix}
\right ]
\end{equation}
      
\begin{equation}
\left [
\begin{matrix}
6 \\\
12 \\\
18
\end{matrix}
\right ]
\left [
\begin{matrix}
7 & 8 & 9
\end{matrix}
\right ] = \left [
\begin{matrix}
42 & 48 & 54 \\\
84 & 96 & 108 \\\
126 & 144 & 162
\end{matrix}
\right ]
\end{equation}

El resultado es:
      
\begin{equation}
\left [
\begin{matrix}
1 \\\
2 \\\
3\
\end{matrix}
\right ]
\left [
\begin{matrix}
4 & 5 & 6
\end{matrix}
\right ]
\left [
\begin{matrix}
7 & 8 & 9
\end{matrix}
\right ] = \left [
\left [
\begin{matrix}
28 & 32 & 36 \\\
56 & 64 & 72 \\\
84 & 96 & 108
\end{matrix}
\right ]
\left [
\begin{matrix}
35 & 40 & 45 \\\
70 & 80 & 90 \\\
105 & 120 & 135
\end{matrix}
\right ]
\left [
\begin{matrix}
42 & 48 & 54 \\\
84 & 96 & 108 \\\
126 & 144 & 162
\end{matrix}
\right ]
\right ]
\end{equation}

### Ejemplo gráfico:


```
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.gca(projection='3d')

ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')

ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')

ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')

ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)

ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')

ax.view_init(17, 24)

plt.show()
```


```
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.gca(projection='3d')

ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')

ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')

ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')

## 4  5  6
## 8 10 12
##12 15 18

ax.text(1, 1, 0, "4", color='magenta')
ax.text(2, 1, 0, "8", color='magenta')
ax.text(3, 1, 0, "12", color='magenta')

ax.text(1, 2, 0, "5", color='orange')
ax.text(2, 2, 0, "10", color='orange')
ax.text(3, 2, 0, "15", color='orange')

ax.text(1, 3, 0, "6", color='purple')
ax.text(2, 3, 0, "12", color='purple')
ax.text(3, 3, 0, "18", color='purple')

ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)

ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')

ax.view_init(17, 24)

plt.show()
```


```
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.gca(projection='3d')

ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')

ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')

ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')

##28 32  36
##56 64  72
##84 96 108
##
## 35  40  45
## 70  80  90
##105 120 135
##
## 42  48  54
## 84  96 108
##126 144 162

ax.text(1, 1, 0, "28", color='magenta')
ax.text(2, 1, 0, "56", color='magenta')
ax.text(3, 1, 0, "84", color='magenta')
ax.text(1, 1, 1, "32", color='magenta')
ax.text(2, 1, 1, "64", color='magenta')
ax.text(3, 1, 1, "96", color='magenta')
ax.text(1, 1, 2, "36", color='magenta')
ax.text(2, 1, 2, "72", color='magenta')
ax.text(3, 1, 2, "108", color='magenta')

ax.text(1, 2, 0, "35", color='orange')
ax.text(2, 2, 0, "70", color='orange')
ax.text(3, 2, 0, "105", color='orange')
ax.text(1, 2, 1, "40", color='orange')
ax.text(2, 2, 1, "80", color='orange')
ax.text(3, 2, 1, "120", color='orange')
ax.text(1, 2, 2, "45", color='orange')
ax.text(2, 2, 2, "90", color='orange')
ax.text(3, 2, 2, "135", color='orange')

ax.text(1, 3, 0, "42", color='purple')
ax.text(2, 3, 0, "84", color='purple')
ax.text(3, 3, 0, "126", color='purple')
ax.text(1, 3, 1, "48", color='purple')
ax.text(2, 3, 1, "96", color='purple')
ax.text(3, 3, 1, "144", color='purple')
ax.text(1, 3, 2, "54", color='purple')
ax.text(2, 3, 2, "108", color='purple')
ax.text(3, 3, 2, "162", color='purple')


ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)

ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')

ax.view_init(17, 24)

plt.show()
```

960008fb823d60b35588e5e63507dcd9a3b2e216
ipynb
Jupyter Notebook
Matrices 3D/Multiplicacion.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
2021-09-28T00:23:45.000Z
2021-09-28T00:23:45.000Z
Matrices 3D/Multiplicacion.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
Matrices 3D/Multiplicacion.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
2015-12-04T12:42:00.000Z
2019-10-31T21:50:32.000Z
Qwen/Qwen-72B
1. YES
2. YES