alleryStart learning →The DIMENSION of $\mathbb{R}^n$ is
A1
Bn
C2n
D$2^n$
Answer & Solution
Correct answer: B. n
1. $\mathbb{R}^n$ has the STANDARD BASIS $e_1, e_2, \ldots, e_n$ where $e_i$ has 1 in position $i$ and 0 elsewhere.
2. So dimension = $n$.
3. Examples: $\mathbb{R}^2 = $ 2D plane (dim 2), $\mathbb{R}^3 = $ 3D space (dim 3).
4. Other options are wrong dimensions.
_Source: Sergei Treil, "Linear Algebra Done Wrong", §2.3 (Dimension)._
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