Matrices & Determinants
Eigenvalues
MMTS_Full_Test_14
Grade 12
Question:
If $\begin{vmatrix}1+x&1&1\\1&1+y&1\\1&1&1+z\end{vmatrix}=0$, then the value of $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}$ is
Step-by-Step Solution
Key Concept: Expand determinant or use row operations
Expand: $xyz+xy+yz+zx+\ldots=0$. $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=-1$.
Correct Answer: 1