hw_9.ipynb

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   "source": [
    "# Домашнее задание по лекции \"Библиотека numpy. Вычислительные задачи.\"\n",
    "\n",
    "## Задание 1 \n",
    "Создайте numpy array с элементами от числа N до 0 (например, для N = 10 это будет array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0]))."
   ]
  },
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   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15\n",
      "[14 13 12 11 10  9  8  7  6  5  4  3  2  1  0]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "N=int(input())\n",
    "x=np.arange(N-1, -1, -1)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Задание 2  \n",
    "Создайте диагональную матрицу с элементами от N до 0. Посчитайте сумму ее значений на диагонали."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "[[4 0 0 0 0]\n",
      " [0 3 0 0 0]\n",
      " [0 0 2 0 0]\n",
      " [0 0 0 1 0]\n",
      " [0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "N=int(input())\n",
    "mat=np.diag(np.arange(N-1, -1, -1)) \n",
    "print(mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Задание 3\n",
    "Решите систему уравнений:  \n",
    "4x + 2y + z = 4  \n",
    "x + 3y = 12  \n",
    "5y + 4z = -3  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.22727273,   7.54545455, -10.18181818])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=np.array([[4, 2, 1], [2, 3, 1], [0, 5, 4]])\n",
    "b=np.array([4, 12, -3])\n",
    "linalg.solve(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose( np.dot(a, linalg.solve(a, b)), b )"
   ]
  }
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