Question

If $\lambda$ is a non real cube root of -2, then the value of $\left|\begin{array}{ccc}1& 2\lambda & 1\\ \lambda & 1& 3{\lambda }^2\\ 2& 2\lambda & 1\end{array}\right|$
is equal to

• A. -11
• B. -12
• C. -13
• D. \N

Answer 1

The correct option is C -13

$\left|\begin{array}{ccc}1& 2\lambda & 1\\ \lambda & 1& 3{\lambda }^2\\ 2& 2\lambda & 1\end{array}\right|$ appliying $R_3\to R_3-R_1$
Then $\left|\begin{array}{ccc}1& 2\lambda & 1\\ {\lambda }^2& 1& 3{\lambda }^2\\ 1& 0& 0\end{array}\right|=6{\lambda }^3-1=6(-2)-1=-13(\because \lambda =(-2{)}^{1/3},\therefore {\lambda }^3=-2)$