The value of the determinant \(\begin{vmatrix}101 & 100 & 3\\ 51 & 50 & 2\\ 21 & 20 & 4\end{vmatrix}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-130\)
Subtracting one column from another does not change the value. Applying \(C_1 \to C_1 - C_2\):
\( \displaystyle \Delta = \begin{vmatrix}1 & 100 & 3\\ 1 & 50 & 2\\ 1 & 20 & 4\end{vmatrix} \)
Taking the common factor 10 out of \(C_2\):
\( \displaystyle \Delta = 10\begin{vmatrix}1 & 10 & 3\\ 1 & 5 & 2\\ 1 & 2 & 4\end{vmatrix} \)
Expanding along the first row:
\(\Delta = 10\big[1(20 - 4) - 10(4 - 2) + 3(2 - 5)\big]\)
\(\Delta = 10(16 - 20 - 9)\)
\(\Delta = -130\)