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

Answer: (A)

$1,-4,7$

$A=\left[\begin{array}{ccc}1& 2& 3\\ 0& -4& 2\\ 0& 0& 7\end{array}\right]$
so,By cayley Hamilton theorem,
$\left[|A-\lambda I|\right]=0$ is characteristic equation
So,$\left|\begin{array}{ccc}1-\lambda & 2& 3\\ 0& \lambda -4& 2\\ 0& 0& 7-\lambda \end{array}\right|=0$
$(1-\lambda )(\lambda -4)(7-\lambda )=0$
so,$\lambda =1,4,+7$.
these are characteristic solution.