Question

The matrix $\left[\begin{array}{ccc}1& 2& 4\\ 3& 0& 6\\ 1& 1& p\end{array}\right]$ has one eigen value equal to 3. The sum of the other two eigen values is

• A. $p$
• B. $p-1$
• C. $p-2$
• D. $p-3$

Answer 1

The correct option is C $p-2$

For any matrix,
Sum of eigen values = sum of the principal diagonal elements (or trace of the matrix)
$\Rightarrow 1+0+p=3+$ sum of other two eigen values
$\Rightarrow$ Sum of other two eigen values
$=p-2$