1. The problem asks: What is the pivot element? 2. In linear algebra, a pivot element is the first non-zero element in a row of a matrix after performing Gaussian elimination or row reduction. 3. The pivot element is used to eliminate the entries below it in the same column to form an upper triangular matrix. 4. For example, in the matrix $$\begin{bmatrix} 2 & 3 & 1 \\ 4 & 7 & 5 \\ 6 & 9 & 8 \end{bmatrix}$$ The pivot element in the first row is $2$ because it is the first non-zero element. 5. After using the pivot to eliminate entries below it, the matrix is transformed step-by-step. 6. The pivot element is crucial for solving systems of linear equations using methods like Gaussian elimination.