What row operation does left-multiplication by the elementary matrix \( \left[\begin{array}{cc}1 & 10 \\ 0 & 1\end{array}\right] \) perform on the matrix \( A \) ? Enter your answer in shorthand symbols.

The given elementary matrix is \[ \left[\begin{array}{cc}1 & 10 \\ 0 & 1\end{array}\right] \] This matrix corresponds to a row operation in the context of matrix algebra. Specifically, it represents the operation of adding 10 times the first row to the second row of any matrix \( A \) that is multiplied by this matrix. In shorthand symbols, the row operation performed by left-multiplication by this elementary matrix is: \[ R_2 \leftarrow R_2 + 10R_1 \] This means that the second row of the matrix \( A \) is replaced by the sum of the second row and 10 times the first row.