The matrix \( \begin{bmatrix}2 & -1 & 3\\\lambda & 0 & 7\\-1 & 1 & 4\end{bmatrix} \) is not invertible for
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \lambda=1 \)
A matrix is not invertible when its determinant is 0. Expanding along the first row:
\( \displaystyle \begin{vmatrix}2 & -1 & 3\\\lambda & 0 & 7\\-1 & 1 & 4\end{vmatrix}=2(0-7)+1(4\lambda+7)+3(\lambda-0) \)
\( \displaystyle =-14+4\lambda+7+3\lambda \)
\( \displaystyle =7\lambda-7 \)
\( \displaystyle 7\lambda-7=0\;\Rightarrow\;\lambda=1 \)