Question:
Using the property of determinants and without expanding, prove that:
$\left|\begin{array}{lll}x & a & x+a \\ y & b & y+b \\ z & c & z+c\end{array}\right|=0$
Solution:
$\left|\begin{array}{lll}x & a & x+a \\ y & b & y+b \\ z & c & z+c\end{array}\right|=0$
$\left|\begin{array}{lll}x & a & x+a \\ y & b & y+b \\ z & c & z+c\end{array}\right|=\left|\begin{array}{lll}x & a & x \\ y & b & y \\ z & c & z\end{array}\right|+\left|\begin{array}{lll}x & a & a \\ y & b & b \\ z & c & c\end{array}\right|=0+0=0$
[Here, the two columns of the determinants are identical]
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.