QJEEM07Ma0b5f: JEE Main 2007 Mathematics - Class 12 JEEM07Ma0b5f Solution: If D =

Question

Verified Solution • 2025–26 Session moderate

If

D = | \begin{matrix} 1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix} |

for

x \ne 0,y \ne 0,

then

D

is :

Accepted Answer

Given,

D = | \begin{matrix} 1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix} |

Apply

\,\,\,{R^2} \to {R_2} - {R_1}

\,\,\,\,

and

\,\,\,\,

R \to {R_3} - {R_1}

\therefore

D = | \begin{matrix} 1 & 1 & 1 \\ 0 & x & 0 \\ 0 & 0 & y \end{matrix} | = x y

Hence,

D

is divisible by both

x

and

y

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