Question

what is the dimension of vector space r over r​

Answer 1

Step-by-step explanation:

For example, the dimension of Rn is n. The dimension of the vector space of polynomials in x with real coefficients having degree at most two is 3. A vector space that consists of only the zero vector has dimension zero. It can be shown that every set of linearly independent vectors in V has size at most dim(V).

Answer 2

Answer:

Vector space R over R has infinite dimensions

Explanation:

We just mentioned that for any positive integer n, R as a vector space over Q contains a collection of linearly independent vectors of size n + 1. As a result, R cannot be a vector space over Q with finite dimension. This means that as a vector space over Q, R has infinite dimension.

For instance, Rₙ has a dimension of n. The vector space of polynomials in x with real coefficients and a maximum degree of two has a dimension of three. A vector space with only the zero vector in it has no dimensions. The size at most dim of each set of linearly independent vectors in V can be demonstrated (V).

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