Consider an original 2-dimensional vector represented as $\mathbf{k} = [4, 7]$. If a transformation function, denoted by $\phi$, is defined as multiplying the first element of an input vector by 2 and adding 1 to the second element, what is the resulting transformed vector $\mathbf{k}'$ after applying the formula $\mathbf{k}' = \phi(\mathbf{k})$?

Vector Transformation Function ($\mathbf{k}'_i = \phi(\mathbf{k}_i)$)

Euclidean Representation of RoPE Transformation

Identifying Components of a Vector Transformation

Match each component of the vector transformation formula $\mathbf{k}'_i = \phi(\mathbf{k}_i)$ with its correct description.