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+# Linear Equations
+Let's consider an linear equation
+$$
+ax=b
+$$
+where $a$ and $b$ are two known constants we can solve for $x$ easily.
+
+## Problem 1
+[]
+
+# Linear Algebra
+Although this isn't a course in linear algebra we are going to use some fundamental concepts from linear algebra to solve systems of equations. 
+
+If you haven't taken linear algebra before, it is the study of linear equations. These equations can be represented in the form of matrices. Let's say we have a system of equation
+$$
+\begin{cases}
+a_{11} x_1 + a_{12} x_2 + a_{13} x_3 = b_1 \\
+a_{21} x_1 + a_{22} x_2 + a_{23} x_3 = b_2 \\
+a_{31} x_1 + a_{32} x_2 + a_{33} x_3 = b_3
+\end{cases}
+
+$$
+We can re-write this into matrix form by creating an $A$ matrix of all $a_{nn}$ values and a $b$ vector as follows
+
+$$
+  A =
+  \left[ {\begin{array}{cc}
+    a_{11} & a_{12} & a_{13}\\
+    a_{21} & a_{22} & a_{23}\\
+    a_{31} & a_{32} & a_{33}\\
+  \end{array} } \right]
+$$
+and
+$$
+  b =
+  \left[ {\begin{array}{cc}
+    b_{1}\\
+    b_{2}\\
+    b_{3}\\
+  \end{array} } \right]
+$$
+to get,
+$$
+Ax=b
+$$
+
+Matrix Math
+
+Matrix definition
+
+
+## Problem 1
+```python
+import numpy as np
+
+# Coefficient matrix A
+A = np.array([[2, 3], [4, 5]])
+# Right - hand side vector b
+b = np.array([4, 6])
+
+# Solve the system of equations
+x = np.linalg.solve(A, b)
+print(x)
+```
+## Problem 2
+
+
+
+
+
 # Systems of Equations
 
+## Working with Systems of Equations
+Matrix Determinates
+Cramer's Rule - 
+Elimination
+
+### Forward Elimination
+### Back Substitution
+### Naive Gauss Elimination
+### Gauss Elimination
+
+### LU Decomposition
+
+## Problem 1
+
+## Problem 2
+
+# LU Decomposition
 
-## Naive Gauss Elimination
+##
 
-## Gauss Elimination
+## Problem 1
 
-## Forward Elimination
+## Problem 2
+Modeling of dynamic systems
 
-## Back Substitution
 
-## LU Decomposition