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Linear algebra is a fundamental pillar of data science. In advanced models in data science, like neural networks, the inputs and transformations are based upon vectors, matrices, and tensors which require a reasonable understanding of linear algebra to get the desired results. It is elegant and the most applied mathematics under the umbrella of data science.

This course teaches linear algebra with a focus on data science. This course encompasses several engaging illustrations, including static images and animations. Furthermore, this course presents mathematical modeling through programming in Python. This course contains several executable coding playgrounds on real data sets and a final project with practical applications.

Aside from theoretical implementations, the modern-day world needs its daunting calculations, trajectory mapping, and distance manipulation, all of which linear algebra provides. By the end of this course, you’ll have a working knowledge of all the necessary teachings in linear algebra.

Linear Algebra for Data Science Using Python

## Statement
Given a system of two linear equations with two unknowns, $w_1$ and $w_2$, determine if there’s a potential solution. In the case of multiple solutions, return the string “There are infinitely many solutions” in the output. In the case of no solution, return the string “Intersection does not exist” in the output.

## Example
Consider an example linear system:

$$2w_1-4w_2=9$$

$$3w_1+7w_2=3$$
The solution to the system is $(w_1,w_2) = (25.5,-10.5)$

## Sample inputs and outputs
The following table describes the desired outputs, given the corresponding inputs to the system above, and a few other examples.



|  Input | Output  |
| :----: | :----: |
| $e1 : [2, 4, 9]$  ,  $e2 : [3, 7, 3]$  | 25.500 , -10.500   |
| $e1 : [2, 2, 4]$  ,  $e2 : [4, 4, 8]$  | There are infinitely many solutions  |
|  $e1 : [2, 4, 9]$ ,  $e2 : [2, 4, 3]$ |  Intersection does not exist |

>**Note:** The output is a string in all cases.


## Try it yourself
The signature of the function is given below. It accepts two arrays containing the scalars of the system of linear equations.


# Statement
Given a system of two linear equations with two unknowns, $w_1$ and $w_2$, determine if there’s a potential solution. In the case of multiple solutions, return the string “There are infinitely many solutions” in the output. In the case of no solution, return the string “Intersection does not exist” in the output.

# Example
Consider an example linear system:

$$2w_1-4w_2=9$$

$$3w_1+7w_2=3$$
The solution to the system is $(w_1,w_2) = (25.5,-10.5)$

# Sample inputs and outputs
The following table describes the desired outputs, given the corresponding inputs to the system above, and a few other examples.



|  Input | Output  |
| :----: | :----: |
| $e1 : [2, 4, 9]$  ,  $e2 : [3, 7, 3]$  | 25.500 , -10.500   |
| $e1 : [2, 2, 4]$  ,  $e2 : [4, 4, 8]$  | There are infinitely many solutions  |
|  $e1 : [2, 4, 9]$ ,  $e2 : [2, 4, 3]$ |  Intersection does not exist |

>**Note:** The output is a string in all cases.


# Try it yourself
The signature of the function is given below. It accepts two arrays containing the scalars of the system of linear equations.


Design a Python algorithm to solve a system of linear equations.

Introduction

Linearity

Matrices

Solving Linear Systems

Singularity

Linear Regression and Least Squares

Vector Space

Vector Spaces of a Matrix

Singular Value Decomposition: SVD

Learning to Find Discriminative Null Space for Face Recognition

Challenge: Linear System Solver

Statement

Example

Sample inputs and outputs

Try it yourself

Input	Output
$e1 : [2, 4, 9]$ , $e2 : [3, 7, 3]$	25.500 , -10.500
$e1 : [2, 2, 4]$ , $e2 : [4, 4, 8]$	There are infinitely many solutions
$e1 : [2, 4, 9]$ , $e2 : [2, 4, 3]$	Intersection does not exist