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Question: \[\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix} \right| =\]...

1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix} \right| =$$
A

1

B

0

C

x

D

xy

Answer

xy

Explanation

Solution

$\left| \begin{matrix} 1 & 1 & 1 \ 1 & 1 + x & 1 \ 1 & 1 & 1 + y \end{matrix} \right| = \left| \begin{matrix} 0 & 0 & 1 \

  • x & x & 1 \ 0 & - y & 1 + y \end{matrix} \right| = xy,$

C1→C1+C2+C3C_{1} \rightarrow C_{1} + C_{2} + C_{3}.