Foundations of Data Science: Linear Algebra

Artificial intelligence (AI) is a branch of computer science that deals with building smart machines or computers that can think, make decisions, and perform tasks with intelligence like human beings. Artificial intelligence develops systems that can perform many types of intelligent tasks, such as voice recognition, face recognition, responding to touch, etc.

Every day, we interact with many AI systems nowadays. For example, Face detection on phones, Voice recognition on Alexa, Apple Siri, or OK Google, FingerPrint detection, recommendation systems on YouTube or Netflix, etc.

These systems sound fascinating. Have you ever thought about how all these systems work?

There is some science behind all these smart systems. To understand artificial intelligence and data science, some mathematical skills are important to learn. Let’s set up a foundation for Data Science with these mathematical concepts and learn them one by one.

Linear Algebra

Linear Algebra is one area of mathematics that is necessary for a thorough grasp of the concepts of Data Science. It is the study of linear combinations, which tries to solve linear equations with the help of vectors and matrices. In the real world, engineers and scientists apply it to various fields of physics and engineering.

Linear algebra describes ways to solve and manipulate systems of linear equations.

Let’s understand linear equations:

We call the above equation a linear equation with two variables, x and y. The term linear because x and y do not have any powers. We call an equation that represents a straight line a linear equation. We can represent the general linear equation as:

Here, a₁, a₂,.. a_n are called coefficients

x₁, x2,…x_n are called variables

b is called the constant

The Solution to the Linear Equation

The solution of the linear equation will be a pair of values. For the equation, x-y = 1, x = 2 and y = 1 is a solution because when we substitute these values in the equation, the equation comes out to be true. Similarly, there can be more pairs that are solutions to the equation.

We can find different pairs of solutions and draw a graph of the linear equation. Let’s find solution pairs in table format by writing different values of y for corresponding values of x.

Table 1.1

When we plot the above x and y pairs on a graph, they form a straight line, as shown below:

Figure 1.1: Line graph of linear equation

Observations

1. Every point whose coordinates satisfy a linear equation lies on the line.
2. Any point that does not lie on the line is not a solution to the linear equation.

Stay Tuned!!

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