Matrices Questions and Answers – Derogatory and Non-Derogatory Matrices

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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,

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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.

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.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn