The value of | array ccc 1 & 1 & 1 1 & 1+x & 1 1 & 1 & 1+y array | is

Correct answer: C. x y | array ccc 1 & 1 & 1 1 & 1+x & 1 1 & 1 & 1+y array | aligned & =[(1+x)(1+y)-1]-1(1+y-1)+1(1-1-x) & =1+x+y+x y-1-y-x & =x y aligned Option (C) is correct.

NDA 2015

Exam: NDA
Year: 2015
Subject: Mathematics
Chapter: Determinants

NDA 2015 · Mathematics · Determinants

The value of | array ccc 1 & 1 & 1 1 & 1+x & 1 1 & 1 & 1+y array |...

The value of

\left|

\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y\end{array}

\right|

is$

Options

A $x+y$
B $x-y$
C $x y$
D $1+x+y$

Correct answer

C. $x y$

Step-by-step solution

\left|

\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\mathrm{x} & 1 \\ 1 & 1 & 1+\mathrm{y}\end{array}

\right|

\begin{aligned} & =[(1+x)(1+y)-1]-1(1+y-1)+1(1-1-x) \\ & =1+x+y+x y-1-y-x \\ & =x y \end{aligned}

\therefore \quad

Option (C) is correct.

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