diff --git a/ex4/Lecture 10 cs229-notes-deep_learning.pdf b/ex4/Lecture 10 cs229-notes-deep_learning.pdf
new file mode 100644
index 0000000..3bb3629
Binary files /dev/null and b/ex4/Lecture 10 cs229-notes-deep_learning.pdf differ
diff --git a/ex4/PE4 - Learning Neural Networks (Exercises).ipynb b/ex4/PE4 - Learning Neural Networks (Exercises).ipynb
index 0480aae..67304d8 100644
--- a/ex4/PE4 - Learning Neural Networks (Exercises).ipynb	
+++ b/ex4/PE4 - Learning Neural Networks (Exercises).ipynb	
@@ -35,7 +35,7 @@
     "\n",
     "Load the data and view some samples in the same way as [ex3](https://github.com/rickwierenga/CS229-Python/tree/master/ex3).\n",
     "\n",
-    "Remember the output of a neural network: $h_\\Theta(x) \\in \\mathbb{R}^K$. We want y to be a 2 dimensional vector in the form that are network should output. For example, we would represent the output 1 as:\n",
+    "Remember the output of a neural network: $h_\\Theta(x) \\in \\mathbb{R}^K$. We want y to be a K dimensional vector in the form that are network should output. For example, we would represent the output 1 as:\n",
     "\n",
     "$\\begin{bmatrix}0\\\\1\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{bmatrix}$"
    ]
@@ -68,6 +68,13 @@
     "y = data[\"y\"]\n",
     "y = y.reshape(len(y))\n",
     "\n",
+    "# ----------NOTE-----------------\n",
+    "# X should have training examples in columns, not rows\n",
+    "# Read also end of page 7 of 'Lecture 10 cs229-notes-deep_learning.pdf', where it says the same thing \n",
+    "# And also the function 'forward' assumes training examples are in columns\n",
+    "X = X.T\n",
+    "\n",
+    "\n",
     "# Initialize some useful variables\n",
     "m, n = X.shape\n",
     "input_layer_size = 400\n",
@@ -112,7 +119,7 @@
     "\n",
     "# get 100 random images from the dataset\n",
     "num_samples = 100\n",
-    "samples = random.sample(list(X), num_samples)\n",
+    "samples = random.sample(list(X.T), num_samples)\n",
     "display_img = Image.new('RGB', (200, 200))\n",
     "\n",
     "# loop over the images, turn them into a PIL image\n",
@@ -168,7 +175,7 @@
     "    return 1 / (1 + np.exp(-z))\n",
     "\n",
     "def add_bias(X):\n",
-    "    m = len(X)\n",
+    "    m = X.shape[1]\n",
     "    bias = np.ones(m)\n",
     "    X = np.vstack((bias, X.T)).T\n",
     "    return X\n",
@@ -670,7 +677,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -684,7 +691,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.1"
+   "version": "3.9.7"
   }
  },
  "nbformat": 4,