Discussion
The determinant of the matrix with rows (1, 2, 3), (4, 5, 6) and (7, 8, 10) is
Answer: B
Expanding along the first row:
\[ \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10 \end{vmatrix} = 1\begin{vmatrix} 5 & 6 \\ 8 & 10 \end{vmatrix} - 2\begin{vmatrix} 4 & 6 \\ 7 & 10 \end{vmatrix} + 3\begin{vmatrix} 4 & 5 \\ 7 & 8 \end{vmatrix} \]
\[ = 1(50-48) - 2(40-42) + 3(32-35) = 2 + 4 - 9 = -3 \]
Changing the last entry from 10 to 9 would make the third row the sum of twice the second less the first, and the determinant would vanish.
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