diff --git a/.ipynb_checkpoints/CE302-Week08-checkpoint.py b/.ipynb_checkpoints/CE302-Week08-checkpoint.py
new file mode 100644
index 0000000..2eef47c
--- /dev/null
+++ b/.ipynb_checkpoints/CE302-Week08-checkpoint.py
@@ -0,0 +1,59 @@
+##############################################
+# 2021_0414-AAD: Multhithreading Example #
+##############################################
+# There are two approaches in code efficiency: 
+# 1. Parallel process : splitting the cpus
+# 2. Creating paralle threads
+###############################
+
+#%% IMPORTS
+
+import os, pandas as pd , time , datetime, numpy as np 
+
+import threading # module for multithreading
+
+#%% 
+exitFlag = 0
+
+class MyThread( threading.Thread) :
+    def __init__( self , threatID , name , my_delay) :
+        threading.Thread.__init__(self)
+        self.threatID = threatID
+        self.name  = name 
+        self.delay = my_delay
+        
+    def run(self):
+        print( f"Starting : {self.name}" )
+
+        print_time( self.name , self.delay , 5 )
+
+        print( f"Exiting : {self.name}")
+
+def print_time( threadName ,  my_delay , counter ):
+
+    while counter :
+        if exitFlag : 
+            threadName.exit()
+        time.sleep( my_delay )
+
+        print( f"{threadName} : time is {time.ctime(time.time())}")
+
+        counter -= 1
+
+#%%
+# Crate the threats
+
+thread_1 = MyThread( 1 , "Thread name 1" , 1)
+
+thread_2 = MyThread( 2 , "Thread name 2" , 5)
+
+# Start the threads
+
+#%%
+
+thread_1.start()
+thread_2.start()
+
+print( f"The file is ok")
+
+# %%
diff --git a/.ipynb_checkpoints/CE302-Week09-checkpoint.ipynb b/.ipynb_checkpoints/CE302-Week09-checkpoint.ipynb
index 899b319..93d8742 100644
--- a/.ipynb_checkpoints/CE302-Week09-checkpoint.ipynb
+++ b/.ipynb_checkpoints/CE302-Week09-checkpoint.ipynb
@@ -6,6 +6,295 @@
    "source": [
     "# CE302 ADVANCED PROGRAMMING TECHNIQUES FOR ENGINEERS"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Create the vectors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vect  = np.array([1,2,3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 2, 3])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vect.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(3,)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vect.T.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Create a matrix from the vectors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vec1 = np.array([1,2,3])\n",
+    "vec2 = np.array([3,4,5])\n",
+    "vec3 = np.array([4,5,6])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Variable   Type       Data/Info\n",
+      "-------------------------------\n",
+      "np         module     <module 'numpy' from '/Us<...>kages/numpy/__init__.py'>\n",
+      "os         module     <module 'os' from '/Users<...>da3/lib/python3.8/os.py'>\n",
+      "sys        module     <module 'sys' (built-in)>\n",
+      "vec1       ndarray    3: 3 elems, type `int64`, 24 bytes\n",
+      "vec2       ndarray    3: 3 elems, type `int64`, 24 bytes\n",
+      "vec3       ndarray    3: 3 elems, type `int64`, 24 bytes\n",
+      "vect       ndarray    3: 3 elems, type `int64`, 24 bytes\n"
+     ]
+    }
+   ],
+   "source": [
+    "whos"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "myMatrice = np.vstack([vec1 , vec2 , vec3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1, 2, 3],\n",
+       "       [3, 4, 5],\n",
+       "       [4, 5, 6]])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 4, 6])"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myMatrice.diagonal()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1, 3, 4],\n",
+       "       [2, 4, 5],\n",
+       "       [3, 5, 6]])"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myMatrice.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(3, 3)"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myMatrice.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Summation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 2,  4,  6],\n",
+       "       [ 6,  8, 10],\n",
+       "       [ 8, 10, 12]])"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myMatrice + myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 2,  4,  6],\n",
+       "       [ 6,  8, 10],\n",
+       "       [ 8, 10, 12]])"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.add( myMatrice , myMatrice)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Subtraction"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[0, 0, 0],\n",
+       "       [0, 0, 0],\n",
+       "       [0, 0, 0]])"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\n",
+    "myMatrice - myMatrice\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/CE302-Week09.ipynb b/CE302-Week09.ipynb
index 899b319..5012020 100644
--- a/CE302-Week09.ipynb
+++ b/CE302-Week09.ipynb
@@ -6,13 +6,697 @@
    "source": [
     "# CE302 ADVANCED PROGRAMMING TECHNIQUES FOR ENGINEERS"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Create the vectors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "error",
+     "ename": "NameError",
+     "evalue": "name 'np' is not defined",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-1-27677bffe019>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mvect\u001b[0m  \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "vect  = np.array([1,2,3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vect.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vect.T.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Create a matrix from the vectors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vec1 = np.array([1,2,3])\n",
+    "vec2 = np.array([3,4,5])\n",
+    "vec3 = np.array([4,5,6])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "whos"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "myMatrice = np.vstack([vec1 , vec2 , vec3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[1, 2, 3],\n",
+       "       [3, 4, 5],\n",
+       "       [4, 5, 6]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 18
+    }
+   ],
+   "source": [
+    "myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "myMatrice.diagonal()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "myMatrice.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "myMatrice.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Summation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 2,  4,  6],\n",
+       "       [ 6,  8, 10],\n",
+       "       [ 8, 10, 12]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 12
+    }
+   ],
+   "source": [
+    "myMatrice + myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 2,  4,  6],\n",
+       "       [ 6,  8, 10],\n",
+       "       [ 8, 10, 12]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 13
+    }
+   ],
+   "source": [
+    "np.add( myMatrice , myMatrice)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Subtraction"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[0, 0, 0],\n",
+       "       [0, 0, 0],\n",
+       "       [0, 0, 0]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 14
+    }
+   ],
+   "source": [
+    "\n",
+    "myMatrice - myMatrice\n"
+   ]
+  },
+  {
+   "source": [
+    "## Division"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[1., 1., 1.],\n",
+       "       [1., 1., 1.],\n",
+       "       [1., 1., 1.]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 15
+    }
+   ],
+   "source": [
+    "myMatrice / myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[1., 1., 1.],\n",
+       "       [1., 1., 1.],\n",
+       "       [1., 1., 1.]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 16
+    }
+   ],
+   "source": [
+    "np.divide( myMatrice , myMatrice)"
+   ]
+  },
+  {
+   "source": [
+    "## Multiplication"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 1,  4,  9],\n",
+       "       [ 9, 16, 25],\n",
+       "       [16, 25, 36]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 17
+    }
+   ],
+   "source": [
+    "myMatrice * myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[1, 2, 3],\n",
+       "       [3, 4, 5],\n",
+       "       [4, 5, 6]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 19
+    }
+   ],
+   "source": [
+    "myMatrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[1., 2., 3.],\n",
+       "       [3., 4., 5.],\n",
+       "       [4., 5., 6.]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 20
+    }
+   ],
+   "source": [
+    "np.sqrt( myMatrice * myMatrice )"
+   ]
+  },
+  {
+   "source": [
+    "### Dot multiplication"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[19, 25, 31],\n",
+       "       [35, 47, 59],\n",
+       "       [43, 58, 73]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 21
+    }
+   ],
+   "source": [
+    "np.dot( myMatrice , myMatrice)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 1,  4,  9],\n",
+       "       [ 9, 16, 25],\n",
+       "       [16, 25, 36]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 22
+    }
+   ],
+   "source": [
+    "np.multiply( myMatrice , myMatrice)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([1, 2, 3])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 23
+    }
+   ],
+   "source": [
+    "vec1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([1, 4, 9])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 24
+    }
+   ],
+   "source": [
+    "vec1 * vec1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 25
+    }
+   ],
+   "source": [
+    "np.dot( vec1 , vec1)"
+   ]
+  },
+  {
+   "source": [
+    "## Determinant "
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "0.0"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 26
+    }
+   ],
+   "source": [
+    "np.linalg.det(myMatrice)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "error",
+     "ename": "LinAlgError",
+     "evalue": "Singular matrix",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-27-66ab86360c61>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m \u001b[0mmyMatrice\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36minv\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m    544\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'D->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    545\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 546\u001b[0;31m     \u001b[0mainv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_umath_linalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    547\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mainv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    548\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m     86\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     87\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     89\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     90\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix"
+     ]
+    }
+   ],
+   "source": [
+    "np.linalg.inv( myMatrice)"
+   ]
+  },
+  {
+   "source": [
+    "## Linear Equations "
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "source": [
+    "3x + 4y + 5z = 10 \n",
+    "\n",
+    "3y - 9z = 0\n",
+    "\n",
+    "x + 10z = 10\n",
+    "\n",
+    "Let's put them in matrix form\n",
+    "\n",
+    "$$ \\begin{bmatrix} 3 & 4 & 5 \\\\ 0 & 3 & -9 \\\\ 1 & 0 & 10 \\end{bmatrix} \\times \\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix} =  \\begin{bmatrix}10\\\\0\\\\10 \\end{bmatrix}$$ \n"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "source": [
+    "**Remember __the Gauss elimination, Gauss-Jordan elimination, LU decomposition__ ...**"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a_matrice = np.array([[3,4,5],[0,3,-9],[1,0,10]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 3,  4,  5],\n",
+       "       [ 0,  3, -9],\n",
+       "       [ 1,  0, 10]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 29
+    }
+   ],
+   "source": [
+    "a_matrice"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "RHS_matrice = np.array([10,0,10])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([-5.38461538,  4.61538462,  1.53846154])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 31
+    }
+   ],
+   "source": [
+    "np.linalg.solve( a_matrice , RHS_matrice)"
+   ]
+  },
+  {
+   "source": [
+    "$$ \\frac{\\begin{bmatrix} 3 & 4 & 5 \\\\ 0 & 3 & -9 \\\\ 1 & 0 & 10 \\end{bmatrix} \\times \\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}}{\\begin{bmatrix} 3 & 4 & 5 \\\\ 0 & 3 & -9 \\\\ 1 & 0 & 10 \\end{bmatrix}} = \\frac {\\begin{bmatrix}10\\\\0\\\\10 \\end{bmatrix} }{\\begin{bmatrix} 3 & 4 & 5 \\\\ 0 & 3 & -9 \\\\ 1 & 0 & 10 \\end{bmatrix} } $$ "
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([[ 0.76923077, -1.02564103, -1.30769231],\n",
+       "       [-0.23076923,  0.64102564,  0.69230769],\n",
+       "       [-0.07692308,  0.1025641 ,  0.23076923]])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 32
+    }
+   ],
+   "source": [
+    "np.linalg.inv(a_matrice)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "array([-5.38461538,  4.61538462,  1.53846154])"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 34
+    }
+   ],
+   "source": [
+    "np.dot( np.linalg.inv( a_matrice), RHS_matrice)"
+   ]
+  },
+  {
+   "source": [
+    "In CE312 class, you'll solve the  [K] . {U} = {P} \n",
+    "\n",
+    "K : stifness matrix\n",
+    "\n",
+    "U : Displacement matrix\n",
+    "\n",
+    "P : Load matrix"
+   ],
+   "cell_type": "markdown",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "39.000000000000014"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 35
+    }
+   ],
+   "source": [
+    "np.linalg.det( a_matrice)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
+   "name": "python385jvsc74a57bd0bdc7d1c825d389c93c370bd8dbc0537723ed308b1e45edf84765b71ae8b74924",
+   "display_name": "Python 3.8.5 64-bit ('anaconda3': virtualenv)"
   },
   "language_info": {
    "codemirror_mode": {
@@ -29,4 +713,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 4
-}
+}
\ No newline at end of file