1. **State the problem:** Find the rank of the matrix using elementary transformations. Given matrix: $$\begin{bmatrix} 1 & 3 & 4 \ \end{bmatrix}$$ 2. **Recall the definition:** The rank of a matrix is the maximum number of linearly independent rows or columns. 3. **Apply elementary row transformations:** Since this matrix has only one row, the rank is 1 if the row is not the zero vector. 4. **Check if the row is zero:** The row is \( [1, 3, 4] \), which is not zero. 5. **Conclusion:** The rank of the matrix is \(1\).