Discussion
The eigenvalues of the diagonal matrix with entries 2, 3 and 7 are
Answer: C
A diagonal matrix is a special case of a triangular one, so its characteristic determinant factorises directly:
\[ \det(A-\lambda I) = (2-\lambda)(3-\lambda)(7-\lambda) = 0 \quad\Rightarrow\quad \lambda = 2,\;3,\;7 \]
Their sum \( 2+3+7=12 \) is the trace and their product \( 2\times3\times7=42 \) the determinant, as the general relations require.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development