1. Tardigrade
  2. Question
  3. Mathematics
  4. Find x, if [ beginmatrix1&2&x 1&1&1 2&1&-1 endmatrix] is singular.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Find $x$, if $\left[\begin{matrix}1&2&x\\ 1&1&1\\ 2&1&-1\end{matrix}\right] $ is singular.

Determinants

Solution:

For singular matrix, $|A| = 0$
$\therefore \quad\left[\begin{matrix}1&2&x\\ 1&1&1\\ 2&1&-1\end{matrix}\right] =0$
$\Rightarrow \quad1\left(-1 - 1 \right) - 2 \left( - 1 -2\right) + x\left(1 -2 \right) = 0$
$\Rightarrow \quad-2+6-x=0 \quad\Rightarrow \quad x=4$