Question

The characteristic roots of the matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 0& -4& 2\\ 0& 0& 7\end{array}\right]$ is/are given by

• A. $1,4,-7$
• B. $1,-4,7$
• C. $-1,4,-7$
• D. $-1,-4,7$

Answer 1

The correct option is B $1,-4,7$

Characteristic equation of $A$ is given by$|A-\lambda I|=0$
$\left|\begin{array}{ccc}1-\lambda & 2& 3\\ 0& -4-\lambda & 2\\ 0& 0& 7-\lambda \end{array}\right|=0$
$\Rightarrow (1-\lambda )(-4-\lambda )(7-\lambda )=0$
$\Rightarrow \lambda =1,-4,7$ are characterstic roots of $A$.