What is Vector space and How to prove vector space bsc maths Be maths || CSIR NET, SET, GATE IIT-JAM
02:04 What is Vector space?
13:50 Example prove that R^n is the Vector space over the field set of real numbers
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what is vector space?
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Example vector space bsc maths
Example : Let 𝑉_𝑛={(𝑥_1, 𝑥_2, 𝑥_3,…, 𝑥_𝑛 )┤| 𝑥_𝑖^′ 𝑠 𝑎𝑟𝑒 𝑠𝑐𝑎𝑙𝑎𝑟𝑠 } be the set of order n-tuples of real numbers, then 𝑉_𝑛 forms a vector space under addition and scalar multiplication defined by
(𝛼_1,𝛼_2,𝛼_3, ….,𝛼_n )+(β_1,β_2,β_3, …,β_n )=(𝛼_1 β_1,𝛼_2 β_2,𝛼_3 β_3, ….,𝛼_n β_n)
And 𝛽(𝛼_1,𝛼_2,𝛼_3, ….,𝛼_n )=(〖𝛽𝛼〗_1,〖𝛽𝛼〗_2,〖𝛽𝛼〗_3, ….,〖𝛽𝛼〗_n)
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