Which of the following is not a valid elementary operation?

The correct option is Rᵢ→1+kRᵢ.

In linear algebra, elementary row operations are operations performed on the rows of a matrix to find equivalent matrices (such as in Gaussian elimination). There are exactly three types of valid elementary row operations:
1. Row Interchange: Swapping the positions of two rows (denoted as $R_i\leftrightarrow R_j$). This corresponds to option 1.
2. Row Addition: Adding a scalar multiple of one row to another row (denoted as $R_i\to R_i+k{R}_j$). Here, option 2 represents a variation where we update a row by adding a scalar multiple of itself or another row, which is a combination of scaling and addition operations.
3. Row Scaling: Multiplying all entries of a row by a non-zero scalar $k$ (denoted as $R_i\to k{R}_i$). This corresponds to option 3.

The operation shown in the correct option, $R_i\to 1+k{R}_i$, involves adding a constant scalar (specifically, the number $1$) to each element of the row. Adding a standalone constant to a row is not a linear operation and is not defined as a valid elementary row operation. Thus, it is not a valid elementary operation.