Determinant: If D=beginvmatrix1&1&1\\1&1+x&1\\1&1&1+yendvmatrix for xneq0 , yneq0… | AIEEE 2007 | Yukti Vault

Yukti Vault

AIEEE 2007 (Offline)Question 1

If $D=\begin{vmatrix}1&1&1\\1&1+x&1\\1&1&1+y\end{vmatrix}$ for $x\neq0$, $y\neq0$, then $D$ is :

Determinant

divisible by $x$ but not $y$divisible by $y$ but not $x$divisible by neither $x$ nor $y$divisible by both $x$ and $y$✓ Correct answer

Solution

Expanding, $D=1\cdot(1+x)(1+y)-\ldots=xy$. Hence $D$ is divisible by both $x$ and $y$.

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