07-求解零空间(Ax=0)：主变量、特解.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = Matrix(([1, 2, 2, 2], [2, 4, 6, 8], [3, 6, 8, 10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}1 & 2 & 0 & -2\\\\0 & 0 & 1 & 2\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\quad \\left [ 0, \\quad 2\\right ]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡1  2  0  -2⎤, [0, 2]⎞\n",
       "⎜⎢           ⎥        ⎟\n",
       "⎜⎢0  0  1  2 ⎥        ⎟\n",
       "⎜⎢           ⎥        ⎟\n",
       "⎝⎣0  0  0  0 ⎦        ⎠"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.rref()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left[\\begin{matrix}-2\\\\1\\\\0\\\\0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}2\\\\0\\\\-2\\\\1\\end{matrix}\\right]\\right ]$$"
      ],
      "text/plain": [
       "⎡⎡-2⎤, ⎡2 ⎤⎤\n",
       "⎢⎢  ⎥  ⎢  ⎥⎥\n",
       "⎢⎢1 ⎥  ⎢0 ⎥⎥\n",
       "⎢⎢  ⎥  ⎢  ⎥⎥\n",
       "⎢⎢0 ⎥  ⎢-2⎥⎥\n",
       "⎢⎢  ⎥  ⎢  ⎥⎥\n",
       "⎣⎣0 ⎦  ⎣1 ⎦⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.nullspace()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing(use_latex='mathjax')\n",
    "\n",
    "#%%\n",
    "A = Matrix(([1, 2, 2, 2], [2, 4, 6, 8], [3, 6, 8, 10]))\n",
    "A\n",
    "\n",
    "#%%\n",
    "A.rref()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}