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The null and inverse vectors

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Consider the set of all entries (a,b,c) where the entries are real numbers.
Addition is defined as:

(a,b,c)+(d,e,f) = (a+d,b+e, c+f)

Scalar multiplication is defined as:

x(a,b,c) = (xa,xb,xc)

Write down the null vector and inverse of (a,b,c).
show that the vectors (a,b,c) do not form a vector space.

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The solution shows how to find the null and inverse vectors using the basic definitions. In addition, we see what is one of the conditions to form a sub-space.

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