Test Index

UPSC NDA Math Model Paper 10

© examsnet.com

Question : 91 of 120

Marks: +1, -0

Find the determinant of the matrix

\begin{vmatrix} x - y & y - z & z - x \\ y - z & z - x & x - y \\ z - x & x - y & y - z \end{vmatrix}

$x + y + z$
$x^{2}+y^{2}+z^{2}$
0
$(x+y+z)^{2} - xyz$

Solution:

\begin{vmatrix} x - y & y - z & z - x \\ y - z & z - x & x - y \\ z - x & x - y & y - z \end{vmatrix}

Apply

R_{1} \rightarrow R_{1} + R_{2} + R_{3}

, We get

\begin{vmatrix} 0 & 0 & 0 \\ y - z & z - x & x - y \\ z - x & x - y & y - z \end{vmatrix}

As we can see that the entry of the first row is zero.

We know that,

If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.

\begin{vmatrix} x - y & y - z & z - x \\ y - z & z - x & x - y \\ z - x & x - y & y - z \end{vmatrix} = 0

© examsnet.com

Go to Question:

Prev Question

Next Question