Question

If $A=\left(\begin{array}{ccc}1& 2& 1\\ -1& 0& 3\\ 2& -1& 1\end{array}\right)$ then characteristic equation is given by

• A. $-{\lambda }^3+2{\lambda }^2-4\lambda +18=0$
• B. ${\lambda }^3+2{\lambda }^2+4\lambda +18=0$
• C. $2{\lambda }^3-{\lambda }^2+6\lambda -2=0$
• D. None of these

Answer 1

The correct option is A $-{\lambda }^3+2{\lambda }^2-4\lambda +18=0$

The characteristic equation of A is given by

$|A-\lambda I|=0$

$\left|\begin{array}{ccc}1-\lambda & 2& 1\\ -1& -\lambda & 3\\ 2& -1& 1-\lambda \end{array}\right|=0$

$(1-\lambda )[-\lambda (1-\lambda )+3]-2(-1(1-\lambda )-6))+1(1+2\lambda )=0$

$\Rightarrow -{\lambda }^3+2{\lambda }^2-4\lambda +18=0$