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Introduction of Vector Space

A vector space is a collection of vectors, which can be added and multiplied (scaled) by the number, which we called scalars. However, the operations of vector addition and scalar multiplication must satisfy the axioms. Here we are going to understand what is vector space and the axioms that we need to meet to handle the operation in vector space.

You can find online video in youtube to understand more, however, here I also shared with you some of the video that i think easy to understand for this topic.

Leave the comment for the attendance.

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1. Introduction of Set Theory : Set and Sub Set

Set Theory is a branch of mathematics that classify items or object that can be grouped into a set. Basically, any object can be collected into a set (A set of students, a set of fruits, a set of car types, etc.). However, Set Theory is applied to an object that can defined the mathematical groups or objects (Sets of Integer, Set of function, etc.)

Before we go further, Here let us learn step by step. First, let us understand what is Set and Sub Set

To understand more, I shared here the youtube video that discussing what is set and subset. .

Please leave a comment after you see the video. I need to know if you are watching this.

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LINEAR COMBINATION, LINEAR DEPENDENCE AND LINEAR INDEPENDENCE

Basic understanding of linear combination is:

(scalar)(x) + (scalar)(y) + (scalar)(z)

Or

(scalar)(x1) + (scalar)(x2) + (scalar)(x3) +….+ (scalar)(xn)

a linear combination of the vectors would be any combination of them using addition and scalar multiplication. A few examples would be:

Here I shared my video slide.

Here some video on youtube discussing about linear vector combination, linear dependence and linear independence.

If this video still cannot help you, you can find another video on youtube that can help you to understand. Anyway, please leave a comment below so that I know you read and watch the video that I put it here.