we can also check if the solution is correct using the np allclose function in [ ]np allclose(np dot(ax)bout[ ]true similarlyfunctions are there for finding the inverse of matrixeigen vectors and eigen values of matrixnorm of matrixdeterminant of matrixand so onsome of which we covered in detail in take look at the details of the function implemented at reference/routines linalg html pandas pandas is an important python library for data manipulationwranglingand analysis it functions as an intuitive and easy-to-use set of tools for performing operations on any kind of data initial work for pandas was done by wes mckinney in while he was developer at aqr capital management since thenthe scope of the pandas project has increased lot and it has become popular library of choice for data scientists all over the world pandas allows you to work with both cross-sectional data and time series based data so let' get started exploring pandasdata structures of pandas all the data representation in pandas is done using two primary data structuresseries dataframes series series in pandas is one-dimensional ndarray with an axis label it means that in functionalityit is almost similar to simple array the values in series will have an index that needs to be hashable this requirement is needed when we perform manipulation and summarization on data contained in series data structure series objects can be used to represent time series data also in this casethe index is datetime object ataframe dataframe is the most important and useful data structurewhich is used for almost all kind of data representation and manipulation in pandas unlike numpy arrays (in generala dataframe can contain heterogeneous data typically tabular data is represented using dataframeswhich is analogous to an excel sheet or sql table this is extremely useful in representing raw datasets as well as processed feature sets in machine learning and data science all the operations can be performed along the axesrowsand columnsin dataframe this will be the primary data structure which we will leveragein most of the use cases in our later