Question

If $\left|\begin{array}{ccc}a+x& a-x& a-x\\ a-x& a+x& a-x\\ a-x& a-x& a+x\end{array}\right|=0$ then $x$ is

• A. $0$
• B. $a$
• C. $3a$
• D. $2a$

Answer 1

Answer: (A), (C)

$0$
$3a$

$=\left|\begin{array}{ccc}(a+x)& 0& (a-x)\\ (a-x)& 2x& (a-x)\\ (a-x)& -2x& (a+x)\end{array}\right|$

Applying $R_2\to R_2+R_3$

$=\left|\begin{array}{ccc}(a+x)& 0& (a-x)\\ 2(a-x)& 0& \left(2a\right)\\ (a-x)& -2x& (a+x)\end{array}\right|$

$=2x(2a^2+2ax-2(a^2+x^2-2ax\left)\right)$

$=2x(2a^2+2ax-2a^2-2x^2+4ax)$

$=4x^2(3a-x)=0$

So, $x=0$ or $x=3a$