Solve left|begin{array}{ccc}1 & x & y 1 & x+y & y 1 & x & x+yend{array}right

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3 and 4 .Determinants and Matrices

medium

Evaluate $\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|$

A

$x y$

B

$x^2 y$

C

$x^2 y^2$

D

$x y^2$

Solution

$\Delta=\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|$

Applying $R_{2} \rightarrow R_{2}-R_{1}$ and $R_{3} \rightarrow R_{3}-R_{1},$ we have:

$\Delta=\left|\begin{array}{lll}1 & x & y \\ 0 & y & 0 \\ 0 & 0 & x\end{array}\right|$

Expanding along $C_{1},$ we have:

$\Delta=1(x y-0)=x y$

Standard 12

Mathematics

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