This topic is the continuations topic of span of a set of the vector. Here the video that explain the topic that can help us to understand the topic.
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Span of a Set of Vectors
Here a few video that discuss about this topic that can help you all to understand more.
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A Set That Is Not A Vector Space
We also need to know what is NOT A VECTOR SPACE because some equation cannot be solve in the vector space. So here we are discussing what type of set that cannot be in a vector space.
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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.
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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.