\documentclass[12pt]{article}

\title{Matrices and Solution of Equations}

\author{FOSSEE}

\begin{document}

\date{}

\vspace{-1in}

\begin{center}

\LARGE{Matrices and Solution of Equations}\\

\large{FOSSEE}

\end{center}

\section{Matrices}

Inputting a Matrix

\begin{verbatim}

In [1]: A = matrix([[1, 2, 3],[4, 5, 6]])

\end{verbatim}

Matrix Operations

\begin{verbatim}

In [1]: A.T # Transpose

In [2]: sum(A) # Sum of all elements

In [3]: A+B # Addition

In [1]: A*B # Product

In [1]: inv(A) # Inverse

In [1]: det(A) # Determinant

\end{verbatim}

Eigen Values and Eigen Vectors

\begin{verbatim}

In [1]: eig(A) #Eigen Values and Vectors

In [2]: eigvals(A) #Eigen Values 

\end{verbatim}

Norm

\begin{verbatim}

In [1]: norm(A)

\end{verbatim}

Single Value Decomposition

\begin{verbatim}

In [1]: svd(A)

\end{verbatim}

Solving a set of equations

\begin{verbatim}

In [1]: A = matrix([...]) # Input Equation Coefficient Matrix   

In [2]: b = matrix([...]) # Equation Target Values

In [3]: x = solve(A, b)

In [4]: Ax = A*x

\end{verbatim}

\end{document}