# 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

Explanation: In this we have,

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

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.