Matrices Questions and Answers – Derogatory and Non-Derogatory Matrices

«
»

This set of Matrices Multiple Choice Questions & Answers (MCQs) focuses on “Derogatory and Non-Derogatory Matrices”.

1. Identify the type of Matrix
\(\begin{bmatrix}7&4&-1\\4&7&-1\\-4&-4&4\end{bmatrix}\)
a) Identity Matrix
b) Non Derogatory Matrix
c) Derogatory Matrix
d) Symmetrical Matrix
View Answer

Answer: c
Explanation: In this we have,

advertisement

A=\(\begin{bmatrix}7&4&-1\\4&7&-1\\-4&-4&4\end{bmatrix}\)

Finding the Characteristic Equation of the matrix
γ3-18γ2+81γ-108=0
Solving the Characteristic equation, we get the Eigenvalues
γ=3,3,12
Since Eigenvalues are repeated, this is a Derogatory Matrix.

advertisement
advertisement

2. Find the Eigenvalues and the type of the given matrix.
A=\(\begin{bmatrix}3&10&5\\-2&-3&-4\\3&5&7\end{bmatrix}\)
a) 3, 1, 3 Non Derogatory
b) 2, 2, 2 Derogatory
c) 3, 2, 2 Derogatory
d) 1, 2, 3 Non Derogatory
View Answer

Answer: c
Explanation: In this we have,
A=\(\begin{bmatrix}3&10&5\\-2&-3&-4\\3&5&7\end{bmatrix}\)
Finding the characteristic equation of the Matrix,
3+3γ2+24γ-141=0
Solving the Characteristic equation, we get the Eigenvalues
γ=3, 2, 2
Since Eigenvalues are repeated, this is a Derogatory Matrix.

Sanfoundry Global Education & Learning Series – Matrices.

advertisement

To practice all areas of Matrices, here is complete set of 1000+ Multiple Choice Questions and Answers.

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & technical discussions at Telegram SanfoundryClasses.