Q95 / 180 · COMEDK 2019 · Mathematics
The characteristic roots of the matrix $\left[\begin{array}{ccc}1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6\end{array}\right]$ are
- Correct answerA1, 3, 6
- B$1,2,4$
- C$4,5,6$
- D$2,4,6$
Solution
We have,
$$
A=\left[\begin{array}{lll}
1 & 0 & 0 \\
2 & 3 & 0 \\
4 & 5 & 6
\end{array}\right]
$$
which is a lower triangular matrix.
Since, characteristic roots of a lower triangular matrix are its diagonal elements.
So, charateristics roots of $A$ are $1,3,6$.
Hence, the correct answer is option: 'A'.