diff --git a/exercise.ipynb b/exercise.ipynb
index 2e5a91b..1835d22 100644
--- a/exercise.ipynb
+++ b/exercise.ipynb
@@ -25,7 +25,14 @@
     "rewrite it in matrix form:\n",
     "\n",
     "\\begin{align*}\n",
-    "        g = \\alpha \\sum_i \\sum_j \\sum_k z_k x_{ij} q_i y_{jk}\n",
+    "        g &= \\alpha \\sum_i \\sum_j \\sum_k z_k x_{ij} q_i y_{jk}\\\\\n",
+    "        &= \\alpha \\sum_i^I \\sum_j^J \\sum_k^K z_k x_{ij} q_i y_{jk}\\qquad (\\text{mit }I,J,K\\in \\mathbb{N})\\\\\n",
+    "        &= Y\\cdot X \\cdot Q \\cdot Z \\cdot \\alpha\\\\\n",
+    "        &= \\begin{bmatrix} y_{11} & \\cdots & y_{1J}\\\\ \\vdots & \\ddots & \\vdots\\\\ y_{K1} & \\cdots & y_{KJ}\\end{bmatrix} \\cdot\n",
+    "        \\begin{bmatrix} x_{11} & \\cdots & x_{1I}\\\\ \\vdots & \\ddots & \\vdots\\\\ x_{J1} & \\cdots & x_{JI}\\end{bmatrix} \\cdot\n",
+    "        \\begin{bmatrix} q_1 \\\\ \\vdots \\\\ q_I\\end{bmatrix} \\cdot\n",
+    "        \\begin{bmatrix} z_1 & \\cdots & z_K\\end{bmatrix} \\cdot\n",
+    "        \\alpha\n",
     "\\end{align*}\n",
     "\n"
    ]
@@ -1004,7 +1011,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.8"
+   "version": "3.8.5"
   }
  },
  "nbformat": 4,