Answer
$14$
Work Step by Step
Deriving this matrix from the original requires two elementary row operations. First, we multiply the second row by $2$, which also doubles the determinant (Theorem 3(c)). Then, we add the first row to the second, which does not change the determinant (Theorem 3(a)). Hence, the determinant of the new matrix is $2\cdot 7=14$.
