22.3: Vectores de base
- Última actualización
- 30 oct 2022
- Guardar como PDF
( \newcommand{\kernel}{\mathrm{null}\,}\)
Considera el siguiente ejemplo. Afirmamos que el siguiente conjunto de vectores forman una base paraR3:
B={(2,1,3),(−1,6,0),(3,4,−10)}
Si estos vectores forman una base, deben ser linealmente independientes y abarcan todo el espacio deR3
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
%matplotlib inline
import matplotlib.pylab as plt
import numpy as np
import sympy as sym
from urllib.request import urlretrieve
sym.init_printing(use_unicode=True)
urlretrieve('https://raw.githubusercontent.com/colbrydi/jupytercheck/master/answercheck.py',
'answercheck.py');
Crea una matriz3×3 numpyA donde las columnas deA form sean los vectores base.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
#Put your answer to the above question here
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
from answercheck import checkanswer checkanswer.matrix(A,'68b81f1c1041158b519936cb1a2e4d6b');
Usando python, calcula el determinante de la matrizA.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
# Put your answer to the above question here.
Usando python, calcule la inversa deA.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
# Put your answer to the above question here.
Usando python, calcule el rango deA.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
# Put your answer to the above question here.
Usando python, calcule la forma de escalón de fila reducida deA.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
# Put your answer to the above question here.
Usando lo anteriorA y el vectorb=(1,3,2). ¿Cuál es la soluciónAx=b?
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
#Put your answer to the above question here.
Login with LibreOne to run this code cell interactively.
If you have already signed in, please refresh the page.
from answercheck import checkanswer checkanswer.matrix(x,'8b0938260dfeaafc9f8e9fec0bc72f17');
Resulta una matriz donde los vectores de columna se forman a partir de vectores base muchas propiedades interesantes y las siguientes declaraciones son equivalentes.
- Los vectores de columnaA forman una base paraRn
- |A|≠0
- Aes invertible.
- Aes fila equivalente aIn (es decir, su forma de escalón de fila reducida esIn)
- El sistema de ecuacionesAx=b tiene una solución única.
- rank(A)=n
No todas las matrices siguen las declaraciones anteriores sino las que sí se utilizan a lo largo del álgebra lineal por lo que es importante que conozcamos estas propiedades.
