Question

Solution set of $\left|\begin{array}{ccc}x& 3& 5\\ 2& 6& 10\\ 7& 21& 35\end{array}\right|=0$ is _________

• A. $\varphi$
• B. $\left(1\right)$
• C. $R$
• D. $\left(0\right)$

Answer 1

Answer: (C)

$R$

$\left|\begin{array}{ccc}x& 3& 5\\ 2& 6& 10\\ 7& 21& 35\end{array}\right|=0$

Performing row operation $R_2\to 7R_2-2R_3$, we get-

$\left|\begin{array}{ccc}x& 3& 5\\ 0& 0& 0\\ 7& 21& 35\end{array}\right|=0$

Since, one row is zero, the determinant of matrix on left side is always $0$ irrespective of the value of $x$.

Hence, $x$ can take any real value.

Solution set =$x\in R$