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   "source": [
    "# Task 04\n",
    "\n",
    "**deadline: 21/03/2021 23:59 CET**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**[0.25 points]:** Edit the conjugate gradient method so that it returns a list of all iterations $ x^{(k)} $ (including the initial guess).\n",
    "\n",
    "**[0.25 points]:** Solve the following system of linear equations \n",
    "\n",
    "$$ \n",
    "4 x_1 + x_2 = 1,\n",
    "$$ \n",
    "\n",
    "$$\n",
    "x_1 + 3x_2 = 2\n",
    "$$\n",
    "\n",
    "using the edited conjugate gradient method withe the error tolerance of $ 10^{-15} $. Print the list of all iterations $ x^{(k)} $.\n",
    "\n",
    "**[0.5 points]:** Plot the iterations $ x^{(k)} $ and the contours of the function \n",
    "\n",
    "$$ \n",
    "f(x) = 1 \\, / \\, 2 \\, x^T \\mathbb{A} x - x^T b, \\ x \\in [-1, 1] \\times [-1, 1],\n",
    "$$\n",
    "\n",
    "where $ \\mathbb{A} $ is the coefficient matrix and $ b $ is the right-hand side vector, using the [`matplotlib.pyplot.scatter`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html) and the [`matplotlib.pyplot.contour`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contour.html) functions, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# add your code here\n"
   ]
  }
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